Closed-loop turbulence control is a critical enabler of aerodynamic drag reduction, lift increase, mixing enhancement, and noise reduction. Current and future applications have epic proportion: cars, trucks, trains, airplanes, wind turbines, medical devices, combustion, chemical reactors, just to name a few. Methods to adaptively adjust open-loop parameters are continually improving toward shorter response times. However, control design for in-time response is challenged by strong nonlinearity, high-dimensionality, and time-delays. Recent advances in the field of model identification and system reduction, coupled with advances in control theory (robust, adaptive, and nonlinear) are driving significant progress in adaptive and in-time closed-loop control of fluid turbulence. In this review, we provide an overview of critical theoretical developments, highlighted by compelling experimental success stories. We also point to challenging open problems and propose potentially disruptive technologies of machine learning and compressive sensing.

References

1.
Fish
,
F. E.
, and
Lauder
,
G. V.
,
2006
, “
Passive and Active Flow Control by Swimming Fishes and Mammals
,”
Annu. Rev. Fluid Mech.
,
38
, pp.
193
224
.
2.
Ahlborn
,
B. K.
,
2004
,
Zoological Physics
,
Springer-Verlag
,
Berlin
.
3.
Dean
,
B.
, and
Bhushan
,
B.
,
2010
, “
Shark-Skin Surfaces for Fluid-Drag Reduction in Turbulent Flow: A Review
,”
Philos. Trans. R. Soc. A
,
368
(
1929
), pp.
4775
4806
.
4.
Bechert
,
D. W.
,
Bruse
,
M.
,
Hage
,
W.
,
van der Hoeven
,
J. G. T.
, and
Hoppe
,
G.
,
1997
, “
Experiments on Drag-Reducing Surfaces and Their Optimization With an Adjustable Geometry
,”
J. Fluid Mech.
,
338
, pp.
59
87
.
5.
Gilliéron
,
P.
, and
Kourta
,
A.
,
2010
, “
Aerodynamic Drag Reduction by Vertical Splitter Plates
,”
Exp. Fluids
,
48
(
1
), pp.
1
16
.
6.
Grandemange
,
M.
,
Ricot
,
D.
,
Vartanian
,
C.
,
Ruiz
,
T.
, and
Cadot
,
O.
,
2014
, “
Characterisation of the Flow Past Real Road Vehicles With Blunt Afterbodies
,”
Int. J. Aerodyn.
,
4
(
1
), pp.
24
42
.
7.
Pfeiffer
,
J.
, and
King
,
R.
,
2012
, “
Multivariable Closed-Loop Flow Control of Drag and Yaw Moment for a 3D Bluff Body
,”
AIAA
Paper No. 2012-2802.
8.
Gad-el Hak
,
M.
,
1989
, “
Flow Control
,”
ASME Appl. Mech. Rev.
,
42
(
10
), pp.
261
293
.
9.
Gad-el Hak
,
M.
, and
Tsai
,
H. M.
,
2006
,
Transition and Turbulence Control
, Vol.
8
,
World Scientific
,
Singapore
.
10.
Kim
,
J.
,
2011
, “
Physics and Control of Wall Turbulence for Drag Reduction
,”
Philos. Trans. R. Soc. A
,
369
(
1940
), pp.
1396
1411
.
11.
Baker
,
C.
,
Jones
,
J.
,
Lopez-Calleja
,
F.
, and
Munday
,
J.
,
2004
, “
Measurements of the Cross Wind Forces on Trains
,”
J. Wind Eng. Ind. Aerodyn.
,
92
(
7
), pp.
547
563
.
12.
Baker
,
C.
,
2010
, “
The Flow Around High Speed Trains
,”
J. Wind Eng. Ind. Aerodyn.
,
98
(
6
), pp.
277
298
.
13.
Schetz
,
J. A.
,
2001
, “
Aerodynamics of High-Speed Trains
,”
Annu. Rev. Fluid Mech.
,
33
(
1
), pp.
371
414
.
14.
Gad-el Hak
,
M.
,
1996
, “
Modern Developments in Flow Control
,”
ASME Appl. Mech. Rev.
,
49
(
7
), pp.
365
379
.
15.
Barber
,
T. J.
,
1999
, private communication.
16.
King
,
R.
,
2007
, “
Active Flow Control
,”
Notes on Numerical Fluid Mechanics and Interdisciplinary Design
, Vol.
95
,
Springer
,
Berlin
.
17.
King
,
R.
,
2010
, “
Active Flow Control II
,”
Notes on Numerical Fluid Mechanics and Interdisciplinary Design
, Vol.
108
,
Springer
,
Berlin
.
18.
Liepmann
,
H.
, and
Nosenchuck
,
D.
,
1982
, “
Active Control of Laminar-Turbulent Transition
,”
J. Fluid Mech.
,
118
, pp.
201
204
.
19.
Roussopoulos
,
K.
,
1993
, “
Feedback Control of Vortex Shedding at Low Reynolds Numbers
,”
J. Fluid Mech.
,
248
, pp.
267
296
.
20.
Kim
,
J.
, and
Bewley
,
T.
,
2007
, “
A Linear Systems Approach to Flow Control
,”
Annu. Rev. Fluid Mech.
,
39
, pp.
383
417
.
21.
Sipp
,
D.
,
Marquet
,
O.
,
Meliga
,
P.
, and
Barbagallo
,
A.
,
2010
, “
Dynamics and Control of Global Instabilities in Open-Flows—A Linearized Approach
,”
ASME Appl. Mech. Rev.
,
63
(
3
), p.
030801
.
22.
Lee
,
C.
,
Kim
,
J.
,
Babcock
,
D.
, and
Goodman
,
R.
,
1997
, “
Application of Neural Networks to Turbulence Control for Drag Reduction
,”
Phys. Fluids
,
9
(
6
), pp.
1740
1747
.
23.
Medjo
,
T. T.
,
Temam
,
R.
, and
Ziane
,
M.
,
2008
, “
Optimal and Robust Control of Fluid Flows: Some Theoretical and Computational Aspects
,”
ASME Appl. Mech. Rev.
,
61
(
1
), p.
010802
.
24.
Bewley
,
T. R.
,
2001
, “
Flow Control: New Challenges for a New Renaissance
,”
Prog. Aerosp. Sci.
,
37
(
1
), pp.
21
58
.
25.
Greenblatt
,
D.
, and
Wygnanski
,
I. J.
,
2000
, “
The Control of Flow Separation by Periodic Excitation
,”
Prog. Aerosp. Sci.
,
36
(
7
), pp.
487
545
.
26.
Bushnell
,
D. M.
, and
McGinley
,
C. B.
,
1989
, “
Turbulence Control in Wall Flows
,”
Annu. Rev. Fluid Mech.
,
21
, pp.
1
20
.
27.
Moin
,
P.
, and
Bewley
,
T.
,
1994
, “
Feedback Control of Turbulence
,”
ASME Appl. Mech. Rev.
,
47
(
6S
), pp.
S3
S13
.
28.
Lumley
,
J.
, and
Blossey
,
P.
,
1998
, “
Control of Turbulence
,”
Annu. Rev. Fluid Mech.
,
30
, pp.
311
327
.
29.
Gutmark
,
E. J.
,
Schadow
,
K. C.
, and
Yu
,
K. H.
,
1994
, “
Methods for Enhanced Turbulence Mixing in Supersonic Shear Flows
,”
ASME Appl. Mech. Rev.
,
47
(
6S
), pp.
S188
S192
.
30.
Aamo
,
O. M.
, and
Krstić
,
M.
,
2002
,
Flow Control by Feedback: Stabilization and Mixing
,
Springer-Verlag
,
London
.
31.
Dimotakis
,
P. E.
,
2005
, “
Turbulent Mixing
,”
Annu. Rev. Fluid Mech.
,
37
, pp.
329
356
.
32.
Mankbadi
,
R. R.
,
1992
, “
Dynamics and Control of Coherent Structures in Turbulent Jets
,”
ASME Appl. Mech. Rev.
,
45
(
6
), pp.
219
248
.
33.
Dowling
,
A. P.
, and
Morgans
,
A. S.
,
2005
, “
Feedback Control of Combustion Oscillations
,”
Annu. Rev. Fluid Mech.
,
37
, pp.
151
182
.
34.
Rowley
,
C.
, and
Williams
,
D.
,
2006
, “
Dynamics and Control of High-Reynolds Number Flows Over Open Cavities
,”
Annu. Rev. Fluid Mech.
,
38
, pp.
251
276
.
35.
Choi
,
H.
,
Jeon
,
W.-P.
, and
Kim
,
J.
,
2008
, “
Control of Flow Over a Bluff Body
,”
Annu. Rev. Fluid Mech.
,
40
, pp.
113
139
.
36.
Cattafesta
,
L.
,
2011
, “
Actuators for Active Flow Control
,”
Annu. Rev. Fluid Mech.
,
43
, pp.
247
272
.
37.
Chen
,
K. K.
, and
Rowley
,
C. W.
,
2011
, “
H2 Optimal Actuator and Sensor Placement in the Linearised Complex Ginzburg-Landau System
,”
J. Fluid Mech.
,
681
, pp.
241
260
.
38.
Bradshaw
,
P.
,
Ferriss
,
D. H.
, and
Johnson
,
R.
,
1964
, “
Turbulence in the Noise-Producing Region of a Circular Jet
,”
J. Fluid Mech.
,
19
(
4
), pp.
591
624
.
39.
Brown
,
G. L.
, and
Roshko
,
A.
,
1974
, “
On Density Effects and Large Structure in Turbulent Mixing Layers
,”
J. Fluid Mech.
,
64
(
4
), pp.
775
816
.
40.
Kim
,
J.
,
2003
, “
Control of Turbulent Boundary Layers
,”
Phys. Fluids
,
15
(
5
), pp.
1093
1105
.
41.
Siauw
,
W.
,
Bonnet
,
J.-P.
,
Tensi
,
J.
,
Cordier
,
L.
,
Noack
,
B. R.
, and
Cattafesta
,
L. I.
,
2010
, “
Transient Dynamics of the Flow Around a NACA0015 Airfoil Using Fluid Vortex Generators
,”
Int. J. Heat Fluid Flow
,
31
(
3
), pp.
450
459
.
42.
Shaqarin
,
T.
,
2014
, private communication.
43.
Choi
,
H.
,
Moin
,
P.
, and
Kim
,
J.
,
1994
, “
Active Turbulence Control for Drag Reduction in Wall-Bounded Flows
,”
J. Fluid Mech.
,
262
, pp.
75
110
.
44.
Gerhard
,
J.
,
Pastoor
,
M.
,
King
,
R.
,
Noack
,
B. R.
,
Dillmann
,
A.
,
Morzyński
,
M.
, and
Tadmor
,
G.
,
2003
, “
Model-Based Control of Vortex Shedding Using Low-Dimensional Galerkin Models
,”
AIAA
Paper No. 2003-4262.
45.
Pastoor
,
M.
,
Henning
,
L.
,
Noack
,
B. R.
,
King
,
R.
, and
Tadmor
,
G.
,
2008
, “
Feedback Shear Layer Control for Bluff Body Drag Reduction
,”
J. Fluid Mech.
,
608
, pp.
161
196
.
46.
Samimy
,
M.
,
Debiasi
,
M.
,
Caraballo
,
E.
,
Serrani
,
A.
,
Yuan
,
X.
,
Little
,
J.
, and
Myatt
,
J.
,
2007
, “
Feedback Control of Subsonic Cavity Flows Using Reduced-Order Models
,”
J. Fluid Mech.
,
579
, pp.
315
346
.
47.
Vukasinovic
,
B.
,
Rusak
,
Z.
, and
Glezer
,
A.
,
2010
, “
Dissipative, Small-Scale Actuation of a Turbulent Shear Layer
,”
J. Fluid Mech.
,
656
, pp.
51
81
.
48.
Luchtenburg
,
D. M.
,
Günter
,
B.
,
Noack
,
B. R.
,
King
,
R.
, and
Tadmor
,
G. A.
,
2009
, “
Generalized Mean-Field Model of the Natural and Actuated Flows Around a High-Lift Configuration
,”
J. Fluid Mech.
,
623
, pp.
283
316
.
49.
Aider
,
J.-L.
,
2014
, private communication.
50.
Gordon
,
M.
, and
Soria
,
J.
,
2002
, “
PIV Measurements of a Zero-Net-Mass-Flux Jet in Cross Flow
,”
Exp. Fluids
,
33
(
6
), pp.
863
872
.
51.
Cater
,
J. E.
, and
Soria
,
J.
,
2002
, “
The Evolution of Round Zero-Net-Mass-Flux Jets
,”
J. Fluid Mech.
,
472
, pp.
167
200
.
52.
Zhang
,
P.
,
Wang
,
J.
, and
Feng
,
L.
,
2008
, “
Review of Zero-Net-Mass-Flux Jet and Its Application in Separation Flow Control
,”
Sci. China Ser. E, Technol. Sci.
,
51
(
9
), pp.
1315
1344
.
53.
Cattafesta
,
L. N.
,
Garg
,
S.
, and
Shukla
,
D.
,
2001
, “
Development of Piezoelectric Actuators for Active Flow Control
,”
AIAA J.
,
39
(
8
), pp.
1562
1568
.
54.
Gallas
,
Q.
,
Holman
,
R.
,
Nishida
,
T.
,
Carroll
,
B.
,
Sheplak
,
M.
, and
Cattafesta
,
L.
,
2003
, “
Lumped Element Modeling of Piezoelectric-Driven Synthetic Jet Actuators
,”
AIAA J.
,
41
(
2
), pp.
240
247
.
55.
Glezer
,
A.
, and
Amitay
,
M.
,
2002
, “
Synthetic Jets
,”
Annu. Rev. Fluid Mech.
,
34
, pp.
503
529
.
56.
Smith
,
B. L.
, and
Glezer
,
A.
,
1998
, “
The Formation and Evolution of Synthetic Jets
,”
Phys. Fluids
,
10
(
9
), pp.
2281
2297
.
57.
Holman
,
R.
,
Utturkar
,
Y.
,
Mittal
,
R.
,
Smith
,
B. L.
, and
Cattafesta
,
L.
,
2005
, “
Formation Criterion for Synthetic Jets
,”
AIAA J.
,
43
(
10
), pp.
2110
2116
.
58.
You
,
D.
, and
Moin
,
P.
,
2008
, “
Active Control of Flow Separation Over an Airfoil Using Synthetic Jets
,”
J. Fluids Struct.
,
24
(
8
), pp.
1349
1357
.
59.
Moreau
,
E.
,
2007
, “
Airflow Control by Non-Thermal Plasma Actuators
,”
J. Phys. D: Appl. Phys.
,
40
(
3
), p.
605
.
60.
Hanson
,
R. E.
,
Lavoie
,
P.
, and
Naguib
,
A. M.
,
2010
, “
Effect of Plasma Actuator Excitation for Controlling Bypass Transition in Boundary Layers
,”
AIAA
Paper No. 2010-1091.
61.
Hanson
,
R. E.
,
Bade
,
K. M.
,
Belson
,
B. A.
,
Lavoie
,
P.
,
Naguib
,
A. M.
, and
Rowley
,
C. W.
,
2014
, “
Feedback Control of Slowly-Varying Transient Growth by an Array of Plasma Actuators
,”
Phys. Fluids
,
26
(
2
), p.
024102
.
62.
Huang
,
J.
,
Corke
,
T. C.
, and
Thomas
,
F. O.
,
2006
, “
Plasma Actuators for Separation Control of Low-Pressure Turbine Blades
,”
AIAA J.
,
44
(
1
), pp.
51
57
.
63.
Roth
,
J. R.
,
Sherman
,
D. M.
, and
Wilkinson
,
S. P.
,
2000
, “
Electrohydrodynamic Flow Control With a Glow-Discharge Surface Plasma
,”
AIAA J.
,
38
(
7
), pp.
1166
1172
.
64.
Post
,
M. L.
, and
Corke
,
T. C.
,
2004
, “
Separation Control on High Angle of Attack Airfoil Using Plasma Actuators
,”
AIAA J.
,
42
(
11
), pp.
2177
2184
.
65.
Hanson
,
R. E.
,
Lavoie
,
P.
,
Naguib
,
A. M.
, and
Morrison
,
J. F.
,
2010
, “
Transient Growth Instability Cancelation by a Plasma Actuator Array
,”
Exp. Fluids
,
49
(
6
), pp.
1339
1348
.
66.
Ho
,
C.-M.
, and
Tai
,
Y.-C.
,
1996
, “
Review: MEMS and Its Applications for Flow Control
,”
ASME J. Fluids Eng.
,
118
(
3
), pp.
437
447
.
67.
Ho
,
C.-M.
, and
Tai
,
Y.-C.
,
1998
, “
Micro-Electro-Mechanical Systems (MEMS) and Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
, pp. 579–612.
68.
Naguib
,
A.
,
Christophorou
,
C.
,
Alnajjar
,
E.
,
Nagib
,
H.
,
Huang
,
C.
, and
Najafi
,
K.
,
1997
, “
Arrays of MEMS-Based Actuators for Control of Supersonic Jet Screech
,”
AIAA
Paper No. 1997-1963.
69.
Löfdahl
,
L.
, and
Gad-el-Hak
,
M.
,
1999
, “
MEMS Applications in Turbulence and Flow Control
,”
Prog. Aeronaut. Sci.
,
35
(
2
), pp.
101
203
.
70.
Huang
,
C.
,
Christophorou
,
C.
,
Najafi
,
K.
,
Naguib
,
A.
, and
Nagib
,
H. M.
,
2002
, “
An Electrostatic Microactuator System for Application in High-Speed Jets
,”
Microelectromech. Syst., J.
,
11
(
3
), pp.
222
235
.
71.
Suzuki
,
H.
,
Kasagi
,
N.
, and
Suzuki
,
Y.
,
2004
, “
Active Control of an Axisymmetric Jet With Distributed Electromagnetic Flap Actuators
,”
Exp. Fluids
,
36
(
3
), pp.
498
509
.
72.
Kasagi
,
N.
,
Suzuki
,
Y.
, and
Fukagata
,
K.
,
2009
, “
Microelectromechanical Systems-Based Feedback Control of Turbulence for Skin Friction Reduction
,”
Annu. Rev. Fluid Mech.
,
41
, pp.
231
251
.
73.
Wu
,
J.
,
Wang
,
L.
, and
Tadmor
,
J.
,
2007
, “
Suppression of the Von Karman Vortex Street Behind a Circular Cylinder by a Traveling Wave Generated by a Flexible Surface
,”
J. Fluid Mech.
,
574
, pp.
365
391
.
74.
Thiria
,
B.
,
Goujon-Durand
,
S.
, and
Wesfreid
,
J. E.
,
2006
, “
The Wake of a Cylinder Performing Rotary Oscillations
,”
J. Fluid Mech.
,
560
, pp.
123
147
.
75.
Bergmann
,
M.
,
Cordier
,
L.
, and
Brancher
,
J.-P.
,
2005
, “
Optimal Rotary Control of the Cylinder Wake Using Proper Orthogonal Decomposition Reduced Order Model
,”
Phys. Fluids
,
17
(
9
), p.
097101
.
76.
Wiener
,
N.
,
1948
,
Cybernetics or Control and Communication in the Animal and the Machine
, 1st ed.,
MIT Press
,
Boston
.
77.
Kolmogorov
,
A.
,
1941
, “
The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number
,”
Dokl. Akad. Nauk. SSSR
,
30
, pp.
9
13
.
78.
Kolmogorov
,
A.
,
1941
, “
On Degeneration (Decay) of Isotropic Turbulence
,”
Dokl. Akad. Nauk SSSR
,
31
, pp.
538
540
.
79.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
,
1987
, “
Fluid Mechanics
,”
Course of Theoretical Physics
, 2nd ed., Vol.
6
,
Pergamon Press
,
Oxford, UK
.
80.
Pope
,
S.
,
2000
,
Turbulent Flows
, 1st ed.,
Cambridge University Press
,
Cambridge, UK
.
81.
Lee
,
M.
,
Malaya
,
N.
, and
Moser
,
R. D.
,
2013
, “
Petascale Direct Numerical Simulation of Turbulent Channel Flow on Up to 786 k Cores
,”
International Conference on High Performance Computing, Networking, Storage and Analysis
(
SC'13
), Denver, CO, Nov. 17–21, p.
61
.
82.
Kaneda
,
Y.
,
Ishihara
,
T.
,
Yokokawa
,
M.
,
Itakura
,
K.
, and
Uno
,
A.
,
2003
, “
Energy Dissipation Rate and Energy Spectrum in High Resolution Direct Numerical Simulations of Turbulence in a Periodic Box
,”
Phys. Fluids
,
15
(
2
), pp.
L21
L24
.
83.
Moore
,
G. E.
,
1965
, “
Cramming More Components Onto Integrated Circuits
,”
Electronics
,
38
(
8
), pp.
114
117
.
84.
Lumley
,
J.
,
1970
,
Stochastic Tools in Turbulence
,
Academic Press
,
New York
.
85.
Holmes
,
P.
,
Lumley
,
J. L.
,
Berkooz
,
G.
, and
Rowley
,
C. W.
,
2012
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.
86.
Sirovich
,
L.
,
1987
, “
Turbulence and the Dynamics of Coherent Structures, Part I—Coherent Structures
,”
Q. Appl. Math.
,
XLV
(
3
), pp.
561
571
.
87.
Golub
,
G. H.
, and
Reinsch
,
C.
,
1970
, “
Singular Value Decomposition and Least Squares Solutions
,”
Numer. Math.
,
14
(
5
), pp.
403
420
.
88.
Golub
,
G.
, and
Kahan
,
W.
,
1965
, “
Calculating the Singular Values and Pseudo-Inverse of a Matrix
,”
J. Soc. Ind. Appl. Math., Ser. B: Numer. Anal.
,
2
(
2
), pp.
205
224
.
89.
Trefethen
,
L. N.
, and
Bau
,
D.
, III.
,
1997
,
Numerical Linear Algebra
, Vol.
50
,
SIAM
,
Philadelphia
.
90.
Antoulas
,
A. C.
,
2005
,
Approximation of Large-Scale Dynamical Systems
,
SIAM
,
Philadelphia
.
91.
Pearson
,
K.
,
1901
, “
On Lines and Planes of Closest Fit to Systems of Points in Space
,”
Philos. Mag.
,
2
(
7–12
), pp.
559
572
.
92.
Hotelling
,
H.
,
1933
, “
Analysis of a Complex of Statistical Variables Into Principal Components
,”
J. Educ. Psychol.
,
24
(
6
), pp.
417
441
.
93.
Karhunen
,
K.
,
1946
, “
Zur Spektraltheorie Stochastischer Prozesse
,”
Ann. Acad. Sci., Fennicae, Ser. A. I., Math.-Phys.
,
37
, pp.
1
79
.
94.
Lorenz
,
E.
,
1956
, “
Empirical Orthogonal Functions and Statistical Weather Prediction
,” Department of Meteorology, Statistical Forecasting Project, MIT, Cambridge, MA, Scientific Report No. 1.
95.
Andino
,
M. Y.
,
Wallace
,
R. D.
,
Glauser
,
M. N.
,
Camphouse
,
R. C.
,
Schmit
,
R. F.
, and
Myatt
,
J. H.
,
2011
, “
Boundary Feedback Flow Control: Proportional Control With Potential Application to Aero-Optics
,”
AIAA J.
,
49
(
1
), pp.
32
40
.
96.
Willcox
,
K.
, and
Peraire
,
J.
,
2002
, “
Balanced Model Reduction Via the Proper Orthogonal Decomposition
,”
AIAA J.
,
40
(
11
), pp.
2323
2330
.
97.
Rowley
,
C.
,
2005
, “
Model Reduction for Fluids Using Balanced Proper Orthogonal Decomposition
,”
Int. J. Bifurcation Chaos
,
15
(
3
), pp.
997
1013
.
98.
Schmid
,
P. J.
, and
Sesterhenn
,
J.
,
2008
, “
Dynamic Mode Decomposition of Numerical and Experimental Data
,”
61st Annual Meeting of the APS Division of Fluid Dynamics, San Antonio, TX, Nov. 23–25, American Physical Society
, College Park, MD, pp. 208.
99.
Schmid
,
P. J.
,
2010
, “
Dynamic Mode Decomposition for Numerical and Experimental Data
,”
J. Fluid Mech.
,
656
, pp.
5
28
.
100.
Rowley
,
C. W.
,
Mezić
,
I.
,
Bagheri
,
S.
,
Schlatter
,
P.
, and
Henningson
,
D.
,
2009
, “
Spectral Analysis of Nonlinear Flows
,”
J. Fluid Mech.
,
645
, pp.
115
127
.
101.
Tu
,
J. H.
,
Rowley
,
C. W.
,
Luchtenburg
,
D. M.
,
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2014
, “
On Dynamic Mode Decomposition: Theory and Applications
,”
J. Comput. Dyn.
,
1
(
2
), pp.
391
421
.
102.
Tu
,
J. H.
,
Rowley
,
C. W.
,
Kutz
,
J. N.
, and
Shang
,
J. K.
,
2014
, “
Spectral Analysis of Fluid Flows Using Sub-Nyquist-Rate PIV Data
,”
Exp. Fluids
,
55
(
9
), p. 1805.
103.
Koopman
,
B. O.
,
1931
, “
Hamiltonian Systems and Transformation in Hilbert Space
,”
Proc. Natl. Acad. Sci.
,
17
(
5
), pp.
315
318
.
104.
Mezić
,
I.
, and
Banaszuk
,
A.
,
2004
, “
Comparison of Systems With Complex Behavior
,”
Phys. D: Nonlinear Phenom.
,
197
(
1
), pp.
101
133
.
105.
Mezić
,
I.
,
2005
, “
Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
,”
Nonlinear Dyn.
,
41
(
1–3
), pp.
309
325
.
106.
Budišić
,
M.
,
Mohr
,
R.
, and
Mezić
,
I.
,
2012
, “
Applied Koopmanism
,”
Chaos: Interdiscip. J. Nonlinear Sci.
,
22
(
4
), p.
047510
.
107.
Mezić
,
I.
,
2013
, “
Analysis of Fluid Flows Via Spectral Properties of the Koopman Operator
,”
Annu. Rev. Fluid Mech.
,
45
, pp.
357
378
.
108.
Schmid
,
P. J.
, and
Hennigson
,
D. S.
,
2001
,
Stability and Transition in Shear Flows
,
Springer
,
New York
.
109.
Schmid
,
P. J.
,
2007
, “
Nonmodal Stability Theory
,”
Annu. Rev. Fluid Mech.
,
39
, pp.
129
162
.
110.
Theofilis
,
V.
,
2011
, “
Global Linear Instability
,”
Annu. Rev. Fluid Mech.
,
43
, pp.
319
352
.
111.
Schmid
,
P. J.
, and
Brandt
,
L.
,
2014
, “
Analysis of Fluid Systems: Stability, Receptivity, Sensitivity
,”
ASME Appl. Mech. Rev.
,
66
(
2
), p.
024803
.
112.
Grosch
,
C. E.
, and
Salwen
,
H.
,
1978
, “
The Continuous Spectrum of the Orr-Sommerfeld Equation Part I—The Spectrum and the Eigenfunctions
,”
J. Fluid Mech.
,
87
, pp.
33
54
.
113.
Salwen
,
H.
, and
Grosch
,
C. E.
,
1981
, “
The Continuous Spectrum of the Orr-Sommerfeld Equation. Part 2—Eigenfunction Expansions
,”
J. Fluid Mech.
,
104
, pp.
445
465
.
114.
Joseph
,
D. D.
,
1976
, “
Stability of Fluid Motions I & II
,”
Springer Tracts in Natural Philosophy
, Vols.
26
and
27
,
Springer
,
New York
.
115.
Boberg
,
L.
, and
Brosa
,
U.
,
1988
, “
Onset of Turbulence in a Pipe
,”
Z. Naturforsch.
,
43a
, pp.
697
726
.
116.
Trefethen
,
L. N.
,
Trefethen
,
A. E.
,
Reddy
,
S. C.
, and
Driscoll
,
T. A.
,
1993
, “
Hydrodynamic Stability Without Eigenvalues
,”
Science
,
261
(
5121
), pp.
578
584
.
117.
Belson
,
B. A.
,
Tu
,
J. H.
, and
Rowley
,
C. W.
,
2014
, “
Algorithm 945: modred—A Parallelized Model Reduction Library
,”
ACM Trans. Math. Software
,
40
(
4
), p.
30
.
118.
von Karman
,
T.
,
1912
, “
Über Den Mechanismus des Widerstands, den Ein Bewegter Korper in Einer Flüssigkeit Erfährt
,”
Göttinger Nachrichten, Math. Phys. Kl.
,
1912
, pp.
547
556
.
119.
Föppl
,
L.
,
1913
, “
Wirbelbewegung hinter einem Kreiszylinder
,”
Sitzb. d. k. Bayer. Akad. d. Wiss.
,
1
, pp. 1.
120.
Suh
,
Y.
,
1993
, “
Periodic Motion of a Point Vortex in a Corner Subject to a Potential Flow
,”
J. Phys. Soc. Jpn.
,
62
, pp.
3441
3445
.
121.
Noack
,
B. R.
,
Mezić
,
I.
,
Tadmor
,
G.
, and
Banaszuk
,
A.
,
2004
, “
Optimal Mixing in Recirculation Zones
,”
Phys. Fluids
,
16
(
4
), pp.
867
888
.
122.
Lugt
,
H.
,
1996
,
Introduction to Vortex Theory
,
Vortex Flow Press
,
Potomac, MA
.
123.
Cottet
,
G. H.
, and
Koumoutsakos
,
P.
,
2000
,
Vortex Methods—Theory and Practice
,
Cambridge University Press
,
Cambridge, UK.
124.
Wu
,
J.-Z.
,
Ma
,
H.-Y.
, and
Zhou
,
M.-D.
,
2006
,
Vorticity and Vortex Dynamics
, 1st ed.,
Springer
,
Berlin
.
125.
Adrian
,
R.
, and
Moin
,
P.
,
1988
, “
Stochastic Estimation of Organized Turbulent Structure: Homogeneous Shear Flow
,”
J. Fluid Mech.
,
190
, pp.
531
559
.
126.
Nicoud
,
F.
,
Baggett
,
J.
,
Moin
,
P.
, and
Cabot
,
W.
,
2001
, “
Large Eddy Simulation Wall-Modeling Based on Suboptimal Control Theory and Linear Stochastic Estimation
,”
Phys. Fluids
,
13
(
10
), pp.
2968
2984
.
127.
Bonnet
,
J.-P.
,
Cole
,
D.
,
Delville
,
J.
,
Glauser
,
M. N.
, and
Ukeiley
,
L. S.
,
1998
, “
Stochastic Estimation and Proper Orthogonal Decomposition—Complementary Techniques for Identfying Structure
,”
Exp. Fluids
,
17
(
5
), pp.
307
314
.
128.
Glauser
,
M. N.
,
Higuchi
,
H.
,
Ausseur
,
J.
, and
Pinier
,
J.
,
2004
, “
Feedback Control of Separated Flows
,”
AIAA
Paper No. 2004-2521.
129.
Ausseur
,
J. M.
,
Pinier
,
J. T.
,
Glauser
,
M. N.
,
Higuchi
,
H.
, and
Carlson
,
H.
,
2006
, “
Experimental Development of a Reduced-Order Model for Flow Separation Control
,”
AIAA
Paper No. 2006-1251.
130.
Tinney
,
C.
,
Coiffet
,
F.
,
Delville
,
J.
,
Hall
,
A.
,
Jordan
,
P.
, and
Glauser
,
M.
,
2006
, “
On Spectral Linear Stochastic Estimation
,”
Exp. Fluids
,
41
(
5
), pp.
763
775
.
131.
Hudy
,
L. M.
,
Naguib
,
A.
, and
Humphreys
,
W. M.
,
2007
, “
Stochastic Estimation of a Separated-Flow Field Using Wall-Pressure-Array Measurements
,”
Phys. Fluids
,
19
(
2
), p.
024103
.
132.
Pinier
,
J. T.
,
Ausseur
,
J. M.
,
Glauser
,
M. N.
, and
Higuchi
,
H.
,
2007
, “
Proportional Closed-Loop Feedback Control of Flow Separation
,”
AIAA J.
,
45
(
1
), pp.
181
190
.
133.
Farrell
,
B. F.
, and
Ioannou
,
P. J.
,
2001
, “
State Estimation Using a Reduced-Order Kalman Filter
,”
J. Atmos. Sci.
,
58
(
23
), pp.
3666
3680
.
134.
King
,
R.
, and
Gilles
,
E.
,
1985
, “
Multiple Kalman Filters for Early Detection of Hazardous States
,”
International Conference Industrial Process Modelling and Control
,
Hangzhou, China
, June 6–9, pp.
130
138
.
135.
Tu
,
J. H.
,
Griffin
,
J.
,
Hart
,
A.
,
Rowley
,
C. W.
,
III
,
L. N. C.
, and
Ukeiley
,
L. S.
,
2013
, “
Integration of Non-Time-Resolved PIV and Time-Resolved Velocity Point Sensors for Dynamic Estimation of Velocity Fields
,”
Exp. Fluids
,
54
(
2
), p. 1429.
136.
Welch
,
G.
, and
Bishop
,
G.
,
1995
, “
An Introduction to the Kalman Filter
,” University of North Carolina, Chapel Hill, NC, Technical Report 95-041.
137.
Busse
,
F. H.
,
1991
, “
Numerical Analysis of Secondary and Tertiary States of Fluid Flow and Their Stability Properties
,”
Appl. Sci. Res.
,
48
(
3–4
), pp.
341
351
.
138.
Noack
,
B. R.
, and
Eckelmann
,
H.
,
1994
, “
A Global Stability Analysis of the Steady and Periodic Cylinder Wake
,”
J. Fluid Mech.
,
270
, pp.
297
330
.
139.
Fletcher
,
C. A. J.
,
1984
,
Computational Galerkin Methods
, 1st ed.,
Springer
,
New York
.
140.
Holmes
,
P.
,
Lumley
,
J. L.
, and
Berkooz
,
G.
,
1998
,
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
, 1st ed.,
Cambridge University Press
,
Cambridge, UK
.
141.
Juang
,
J. N.
, and
Pappa
,
R. S.
,
1985
, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction
,”
J. Guid., Control, Dyn.
,
8
(
5
), pp.
620
627
.
142.
Juang
,
J. N.
,
1994
,
Applied System Identification
,
Prentice-Hall
,
Upper Saddle River, NJ
.
143.
Ljung
,
L.
,
2001
, “
Black-Box Models From Input–Output Measurements
,”
18th IEEE Instrumentation and Measurement Technology Conference
(
IMTC 2001
),
Budapest
, May 21–23, pp.
138
146
.
144.
Ljung
,
L.
,
1999
,
System Identification: Theory for the User
,
Prentice-Hall
,
Upper Saddle River, NJ
.
145.
Crouch
,
P.
,
1981
, “
Dynamical Realizations of Finite Volterra Series
,”
SIAM J. Control Optim.
,
19
(
2
), pp.
177
202
.
146.
Boyd
,
S.
,
Chua
,
L. O.
, and
Desoer
,
C. A.
,
1984
, “
Analytical Foundations of Volterra Series
,”
IMA J. Math. Control Inf.
,
1
(
3
), pp.
243
282
.
147.
Boyd
,
S.
, and
Chua
,
L. O.
,
1985
, “
Fading Memory and the Problem of Approximating Nonlinear Operators With Volterra Series
,”
IEEE Trans. Circuits Syst.
,
32
(
11
), pp.
1150
1161
.
148.
Lesiak
,
C.
, and
Krener
,
A. J.
,
1978
, “
The Existence and Uniqueness of Volterra Series for Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
23
(
6
), pp.
1090
1095
.
149.
Brockett
,
R. W.
,
1976
, “
Volterra Series and Geometric Control Theory
,”
Automatica
,
12
(
2
), pp.
167
176
.
150.
Krstić
,
M.
,
Smyshlyaev
,
A.
, and
Vazquez
,
R.
,
2006
, “
Boundary Control of PDEs and Applications to Turbulent Flows and Flexible Structures
,”
IEEE Chinese Control Conference
(
CCC 2006
), Harbin, China, Aug. 7–11, pp.
PL–4
PL–16
.
151.
Floriani
,
E.
,
de Wit
,
T. D.
, and
Le Gal
,
P.
,
2000
, “
Nonlinear Interactions in a Rotating Disk Flow: From a Volterra Model to the Ginzburg–Landau Equation
,”
Chaos: Interdiscip. J. Nonlinear Sci.
,
10
(
4
), pp.
834
847
.
152.
Tromp
,
J. C.
, and
Jenkins
,
J. E. A.
,
1990
, “
Volterra Kernel Identification Scheme Applied to Aerodynamic Reactions
,”
AIAA
Paper No. 90-2803.
153.
Prazenica
,
R. J.
,
Reisenthel
,
P. H.
,
Kurdila
,
A. J.
, and
Brenner
,
M. J.
,
2007
, “
Volterra Kernel Extrapolation for Modeling Nonlinear Aeroelastic Systems at Novel Flight Conditions
,”
J. Aircr.
,
44
(
1
), pp.
149
162
.
154.
Balajewicz
,
M.
, and
Dowell
,
E.
,
2012
, “
Reduced-Order Modeling of Flutter and Limit-Cycle Oscillations Using the Sparse Volterra Series
,”
J. Aircr.
,
49
(
6
), pp.
1803
1812
.
155.
Balikhin
,
M.
,
Bates
,
I.
, and
Walker
,
S.
,
2001
, “
Identification of Linear and Nonlinear Processes in Space Plasma Turbulence Data
,”
Adv. Space Res.
,
28
(
5
), pp.
787
800
.
156.
Vazquez
,
R.
, and
Krstić
,
M.
,
2007
,
Control of Turbulent and Magnetohydrodynamic Channel Flows: Boundary Stabilization and State Estimation
,
Springer
,
New York
.
157.
Estrada
,
T.
,
Happel
,
T.
,
Hidalgo
,
C.
,
Ascasibar
,
E.
, and
Blanco
,
E.
,
2010
, “
Experimental Observation of Coupling Between Turbulence and Sheared Flows During LH Transitions in a Toroidal Plasma
,”
Europhys. Lett.
,
92
(
3
), p.
35001
.
158.
Smola
,
A. J.
, and
Schölkopf
,
B.
,
2004
, “
A Tutorial on Support Vector Regression
,”
Stat. Comput.
,
14
(
3
), pp.
199
222
.
159.
Schölkopf
,
B.
, and
Smola
,
A. J.
,
2002
,
Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
,
MIT Press
, Cambridge, MA.
160.
Suykens
,
J. A.
, and
Vandewalle
,
J.
,
1999
, “
Least Squares Support Vector Machine Classifiers
,”
Neural Process. Lett.
,
9
(
3
), pp.
293
300
.
161.
Doyle
,
J. C.
,
1978
, “
Guaranteed Margins for LQG Regulators
,”
IEEE Trans. Autom. Control
,
23
(
4
), pp.
756
757
.
162.
Doyle
,
J. C.
, and
Stein
,
G.
,
1981
, “
Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis
,”
IEEE Trans. Autom. Control
,
26
(
1
), pp.
4
16
.
163.
Glover
,
K.
, and
Doyle
,
J. C.
,
1988
, “
State-Space Formulae for All Stabilizing Controllers That Satisfy an H∞-Norm Bound and Relations to Risk Sensitivity
,”
Syst. Control Lett.
,
11
(
3
), pp.
167
172
.
164.
Doyle
,
J. C.
,
Glover
,
K.
,
Khargonekar
,
P. P.
, and
Francis
,
B. A.
,
1989
, “
State-Space Solutions to Standard H2 and H∞ Control Problems
,”
IEEE Trans. Autom. Control
,
34
(
8
), pp.
831
847
.
165.
Schlinker
,
R.
,
Simonich
,
J.
,
Shannon
,
D.
,
Reba
,
R.
,
Colonius
,
T.
,
Gudmundsson
,
K.
, and
Ladeinde
,
F.
,
2009
, “
Supersonic Jet Noise From Round and Chevron Nozzles: Experimental Studies
,”
AIAA
Paper No. 2009-3257.
166.
Skogestad
,
S.
, and
Postlethwaite
,
I.
,
1996
,
Multivariable Feedback Control
,
Wiley
,
Chichester, UK
.
167.
Dullerud
,
G. E.
, and
Paganini
,
F.
,
2000
, “
A Course in Robust Control Theory: A Convex Approach
,”
Texts in Applied Mathematics
,
Springer
,
Berlin
.
168.
Scott Collis
,
S.
,
Joslin
,
R. D.
,
Seifert
,
A.
, and
Theofilis
,
V.
,
2004
, “
Issues in Active Flow Control: Theory, Control, Simulation, and Experiment
,”
Prog. Aerosp. Sci.
,
40
(
4
), pp.
237
289
.
169.
Rowley
,
C. W.
, and
Batten
,
B. A.
,
2008
, “
Dynamic and Closed-Loop Control
,”
Fundamentals and Applications of Modern Flow Control
(Progress in Astronautics and Aeronautics, Vol. 231), American Institute of Aeronautics and Astronautics, Reston, VA, pp. 115–148.
170.
Bagheri
,
S.
,
Hoepffner
,
J.
,
Schmid
,
P. J.
, and
Henningson
,
D. S.
,
2009
, “
Input–Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows
,”
ASME Appl. Mech. Rev.
,
62
(
2
), p.
020803
.
171.
Fabbiane
,
N.
,
Semeraro
,
O.
,
Bagheri
,
S.
, and
Henningson
,
D. S.
,
2014
, “
Adaptive and Model-Based Control Theory Applied to Convectively Unstable Flows
,”
ASME Appl. Mech. Rev.
,
66
(
6
), p.
060801
.
172.
Devasia
,
S.
,
Chen
,
D.
, and
Paden
,
B.
,
1996
, “
Nonlinear Inversion-Based Output Tracking
,”
IEEE Trans. Autom. Control
,
41
(
7
), pp.
930
942
.
173.
Krstić
,
M.
, and
Banaszuk
,
A.
,
2006
, “
Multivariable Adaptive Control of Instabilities Arising in Jet Engines
,”
Control Eng. Pract.
,
14
(
7
), pp.
833
842
.
174.
Bewley
,
T. R.
,
Temam
,
R.
, and
Ziane
,
M.
,
2000
, “
A General Framework for Robust Control in Fluid Mechanics
,”
Phys. D
,
138
(
3–4
), pp.
360
392
.
175.
King
,
R.
,
Active Flow and Combustion Control
, Vol.
127
,
Springer International Publishing
,
Cham, Switzerland
.
176.
Kerstens
,
W.
,
Pfeiffer
,
J.
,
Williams
,
D.
,
King
,
R.
, and
Colonius
,
T.
,
2011
, “
Closed-Loop Control of Lift for Longitudinal Gust Suppression at Low Reynolds Numbers
,”
AIAA J.
,
49
(
8
), pp.
1721
1728
.
177.
Devasia
,
S.
,
2002
, “
Should Model-Based Inverse Inputs be Used as Feedforward Under Plant Uncertainty?
IEEE Trans., Autom. Control
,
47
(
11
), pp.
1865
1871
.
178.
Chen
,
K. K.
, and
Rowley
,
C. W.
,
2013
, “
Normalized Coprime Robust Stability and Performance Guarantees for Reduced-Order Controllers
,”
IEEE Trans. Autom. Control
,
58
(
4
), pp.
1068
1073
.
179.
Businger
,
P. A.
, and
Golub
,
G. H.
,
1969
, “
Algorithm 358: Singular Value Decomposition of a Complex Matrix [F1, 4, 5]
,”
Commun. ACM
,
12
(
10
), pp.
564
565
.
180.
Ho
,
B. L.
, and
Kalman
,
R. E.
,
1965
, “
Effective Construction of Linear State-Variable Models From Input/Output Data
,”
3rd Annual Allerton Conference on Circuit and System Theory
, Monticello, IL, Oct. 20–22, pp.
449
459
.
181.
Moore
,
B. C.
,
1981
, “
Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction
,”
IEEE Trans. Autom. Control
,
26
(
1
), pp.
17
32
.
182.
Berkooz
,
G.
,
Holmes
,
P.
, and
Lumley
,
J.
,
1993
, “
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
25
, pp.
539
575
.
183.
Ilak
,
M.
, and
Rowley
,
C. W.
,
2008
, “
Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
,”
Phys. Fluids
,
20
(
3
), p.
034103
.
184.
Lall
,
S.
,
Marsden
,
J. E.
, and
Glavaški
,
S.
,
1999
, “
Empirical Model Reduction of Controlled Nonlinear Systems
,”
International Federation of Automatic Control (IFAC) World Congress
, Beijing, July 5–9, pp.
473
478
.
185.
Lall
,
S.
,
Marsden
,
J. E.
, and
Glavaški
,
S.
,
2002
, “
A Subspace Approach to Balanced Truncation for Model Reduction of Nonlinear Control Systems
,”
Int. J. Rob. Nonlinear Control
,
12
(
6
), pp.
519
535
.
186.
Laub
,
A. J.
,
Heath
,
M. T.
,
Paige
,
C.
, and
Ward
,
R.
,
1987
, “
Computation of System Balancing Transformations and Other Applications of Simultaneous Diagonalization Algorithms
,”
IEEE Trans. Autom. Control
,
32
(
2
), pp.
115
122
.
187.
Sirovich
,
L.
,
1987
, “
Turbulence and the Dynamics of Coherent Structures, Part III—Dynamics and Scaling
,”
Q. Appl. Math.
,
XLV
, pp.
583
590
.
188.
Sirovich
,
L.
,
1987
, “
Turbulence and the Dynamics of Coherent Structures, Part II—Symmetries and Transformations
,”
Q. Appl. Math.
,
XLV
, pp.
573
582
.
189.
Ma
,
Z.
,
Ahuja
,
S.
, and
Rowley
,
C. W.
,
2011
, “
Reduced Order Models for Control of Fluids Using the Eigensystem Realization Algorithm
,”
Theor. Comput. Fluid Dyn.
,
25
(
1
), pp.
233
247
.
190.
Luchtenburg
,
D. M.
, and
Rowley
,
C. W.
,
2011
, “
Model Reduction Using Snapshot-Based Realizations
,”
Bull. Am. Phys. Soc.
,
56
, p. BAPS.2011.DFD.H19.4.
191.
Tu
,
J. H.
, and
Rowley
,
C. W.
,
2012
, “
An Improved Algorithm for Balanced POD Through an Analytic Treatment of Impulse Response Tails
,”
J. Comput. Phys.
,
231
(
16
), pp.
5317
5333
.
192.
Juang
,
J. N.
,
Phan
,
M.
,
Horta
,
L. G.
, and
Longman
,
R. W.
,
1991
, “
Identification of Observer/Kalman Filter Markov Parameters: Theory and Experiments
,” NASA Langley Research Center, Hampton, VA,
NASA
Technical Memorandum No. 104069.
193.
Phan
,
M.
,
Juang
,
J. N.
, and
Longman
,
R. W.
,
1992
, “
Identification of Linear-Multivariable Systems by Identification of Observers With Assigned Real Eigenvalues
,”
J. Astronaut. Sci.
,
40
(
2
), pp.
261
279
.
194.
Phan
,
M.
,
Horta
,
L. G.
,
Juang
,
J. N.
, and
Longman
,
R. W.
,
1993
, “
Linear System Identification Via an Asymptotically Stable Observer
,”
J. Optim. Theory Appl.
,
79
(
1
), pp.
59
86
.
195.
Proctor
,
J. L.
,
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2014
, “
Dynamic Mode Decomposition With Control: Using State and Input Snapshots to Discover Dynamics
,”
arXiv:1409.6358
.
196.
Barkley
,
D.
, and
Tuckerman
,
L. S.
,
1999
, “
Stability Analysis of Perturbed Plane Couette Flow
,”
Phys. Fluids
,
11
(
5
), pp.
1187
1195
.
197.
Bayly
,
B. J.
,
Orszag
,
S. A.
, and
Herbert
,
T.
,
1988
, “
Instability Mechanisms in Shear-Flow Transition
,”
Annu. Rev. Fluid Mech.
,
20
(
1
), pp.
359
391
.
198.
Orszag
,
S. A.
, and
Patera
,
A. T.
,
1983
, “
Secondary Instability of Wall-Bounded Shear Flows
,”
J. Fluid Mech.
,
128
, pp.
347
385
.
199.
Ruelle
,
D.
, and
Takens
,
F.
,
1971
, “
On the Nature of Turbulence
,”
Commun. Math. Phys.
,
20
(
3
), pp.
167
192
.
200.
Aamo
,
O. M.
,
Krstić
,
M.
, and
Bewley
,
T. R.
,
2003
, “
Control of Mixing by Boundary Feedback in 2D Channel Flow
,”
Automatica
,
39
(
9
), pp.
1597
1606
.
201.
Bagheri
,
S.
, and
Henningson
,
D. S.
,
2011
, “
Transition Delay Using Control Theory
,”
Philos. Trans. R. Soc. A
,
369
(
1940
), pp.
1365
1381
.
202.
Abergel
,
F.
, and
Temam
,
R.
,
1990
, “
On Some Control Problems in Fluid Mechanics
,”
Theor. Comput. Fluid Dyn.
,
1
(
6
), pp.
303
325
.
203.
Jameson
,
A.
,
2003
, “
Aerodynamic Shape Optimization Using the Adjoint Method
” (VKI Lecture Series on Aerodynamic Drag Prediction and Reduction), von Karman Institute of Fluid Dynamics, Rhode-St-Genese, Belgium.
204.
Reuther
,
J. J.
,
Jameson
,
A.
,
Alonso
,
J. J.
,
Rimlinger
,
M. J.
, and
Saunders
,
D.
,
1999
, “
Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers, Part 1
,”
J. Aircr.
,
36
(
1
), pp.
51
60
.
205.
Jameson
,
A.
,
Martinelli
,
L.
, and
Pierce
,
N.
,
1998
, “
Optimum Aerodynamic Design Using the Navier–Stokes Equations
,”
Theor. Comput. Fluid Dyn.
,
10
(
1–4
), pp.
213
237
.
206.
Reuther
,
J.
,
Jameson
,
A.
,
Farmer
,
J.
,
Martinelli
,
L.
, and
Saunders
,
D.
,
1996
, “
Aerodynamic Shape Optimization of Complex Aircraft Configurations Via an Adjoint Formulation
,” Research Institute for Advanced Computer Science,
NASA
Ames Research Center, Mountain View, CA, Report No. NASA-CR-203275.
207.
Choi
,
H.
,
Temam
,
R.
,
Moin
,
P.
, and
Kim
,
J.
,
1993
, “
Feedback Control for Unsteady Flow and Its Application to the Stochastic Burgers Equation
,”
J. Fluid Mech.
,
253
, pp.
509
543
.
208.
Bewley
,
T.
, and
Moin
,
P.
,
1994
, “
Optimal Control of Turbulent Channel Flows
,”
Act. Control Vib. Noise
, ASME DE-Vol. 75, pp.
221
227
.
209.
Lee
,
C.
,
Kim
,
J.
, and
Choi
,
H.
,
1998
, “
Suboptimal Control of Turbulent Channel Flow for Drag Reduction
,”
J. Fluid Mech.
,
358
, pp.
245
258
.
210.
Bewley
,
T. R.
,
Moin
,
P.
, and
Temam
,
R.
,
2001
, “
DNS-Based Predictive Control of Turbulence: An Optimal Benchmark for Feedback Algorithms
,”
J. Fluid Mech.
,
447
, pp.
179
225
.
211.
Collis
,
S. S.
,
Chang
,
Y.
,
Kellogg
,
S.
, and
Prabhu
,
R.
,
2000
, “
Large Eddy Simulation and Turbulence Control
,”
AIAA
Paper No. 2000-2564.
212.
Bewley
,
T.
, and
Liu
,
S.
,
1998
, “
Optimal and Robust Control and Estimation of Linear Paths to Transition
,”
J. Fluid Mech.
,
365
, pp.
305
349
.
213.
Baramov
,
L.
,
Tutty
,
O. R.
, and
Rogers
,
E.
,
2000
, “
Robust Control of Plane Poiseuille Flow
,”
AIAA
Paper No. 2000-2684.
214.
Högberg
,
M.
,
Bewley
,
T. R.
, and
Henningson
,
D. S.
,
2003
, “
Linear Feedback Control and Estimation of Transition in Plane Channel Flow
,”
J. Fluid Mech.
,
481
, pp.
149
175
.
215.
Högberg
,
M.
, and
Henningson
,
D. S.
,
2002
, “
Linear Optimal Control Applied to Instabilities in Spatially Developing Boundary Layers
,”
J. Fluid Mech.
,
470
, pp.
151
179
.
216.
Chevalier
,
M.
,
Hœpffner
,
J.
,
Åkervik
,
E.
, and
Henningson
,
D.
,
2007
, “
Linear Feedback Control and Estimation Applied to Instabilities in Spatially Developing Boundary Layers
,”
J. Fluid Mech.
,
588
, pp.
163
187
.
217.
Åkervik
,
E.
,
Hœpffner
,
J.
,
Ehrenstein
,
U.
, and
Henningson
,
D. S.
,
2007
, “
Optimal Growth, Model Reduction and Control in Separated Boundary-Layer Flow Using Global Eigenmodes
,”
J. Fluid Mech.
,
579
, pp.
305
314
.
218.
Ahuja
,
S.
,
Rowley
,
C. W.
,
Kevrekidis
,
I. G.
,
Wei
,
M.
,
Colonius
,
T.
, and
Tadmor
,
G.
,
2007
, “
Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models
,”
AIAA
Paper No. 2007-709.
219.
Colonius
,
T.
, and
Taira
,
K.
,
2008
, “
A Fast Immersed Boundary Method Using a Nullspace Approach and Multi-Domain Far-Field Boundary Conditions
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
25–28
), pp.
2131
2146
.
220.
Taira
,
K.
, and
Colonius
,
T.
,
2007
, “
The Immersed Boundary Method: A Projection Approach
,”
J. Comput. Phys.
,
225
(
2
), pp.
2118
2137
.
221.
Bagheri
,
S.
,
Brandt
,
L.
, and
Henningson
,
D.
,
2009
, “
Input–Output Analysis, Model Reduction and Control of the Flat-Plate Boundary Layer
,”
J. Fluid Mech.
,
620
, pp.
263
298
.
222.
Semeraro
,
O.
,
Bagheri
,
S.
,
Brandt
,
L.
, and
Henningson
,
D. S.
,
2011
, “
Feedback Control of Three-Dimensional Optimal Disturbances Using Reduced-Order Models
,”
J. Fluid Mech.
,
677
, pp.
63
102
.
223.
Illingworth
,
S. J.
,
Morgans
,
A. S.
, and
Rowley
,
C. W.
,
2010
, “
Feedback Control of Flow Resonances Using Balanced Reduced-Order Models
,”
J. Sound Vib.
,
330
(
8
), pp.
1567
1581
.
224.
Illingworth
,
S. J.
,
Morgans
,
A. S.
, and
Rowley
,
C. W.
,
2012
, “
Feedback Control of Cavity Flow Oscillations Using Simple Linear Models
,”
J. Fluid Mech.
,
709
, pp.
223
248
.
225.
Semeraro
,
O.
,
Bagheri
,
S.
,
Brandt
,
L.
, and
Henningson
,
D. S.
,
2013
, “
Transition Delay in a Boundary Layer Flow Using Active Control
,”
J. Fluid Mech.
,
731
, pp.
288
311
.
226.
Moarref
,
R.
, and
Jovanović
,
M. R.
,
2012
, “
Model-Based Design of Transverse Wall Oscillations for Turbulent Drag Reduction
,”
J. Fluid Mech.
,
707
, pp.
205
240
.
227.
Cortelezzi
,
L.
,
Lee
,
K.
,
Kim
,
J.
, and
Speyer
,
J.
,
1998
, “
Skin-Friction Drag Reduction Via Robust Reduced-Order Linear Feedback Control
,”
Int. J. Comput. Fluid Dyn.
,
11
(
1–2
), pp.
79
92
.
228.
Cortelezzi
,
L.
, and
Speyer
,
J.
,
1998
, “
Robust Reduced-Order Controller of Laminar Boundary Layer Transitions
,”
Phys. Rev. E
,
58
(
2
), pp.
1906
1910
.
229.
Lee
,
K. H.
,
Cortelezzi
,
L.
,
Kim
,
J.
, and
Speyer
,
J.
,
2001
, “
Application of Reduced-Order Controller to Turbulent Flows for Drag Reduction
,”
Phys. Fluids
,
13
(
5
), pp.
1321
1330
.
230.
Kasagi
,
N.
,
Hasegawa
,
Y.
, and
Fukagata
,
K.
,
2009
, “
Toward Cost-Effective Control of Wall Turbulence for Skin Friction Drag Reduction
,”
Advances in Turbulence XII
,
Springer
,
Berlin
, pp.
189
200
.
231.
Fukagata
,
K.
,
Kobayashi
,
M.
, and
Kasagi
,
N.
,
2010
, “
On the Friction Drag Reduction Effect by a Control of Large-Scale Turbulent Structures
,”
J. Fluid Sci. Technol.
,
5
(
3
), pp.
574
584
.
232.
Mamori
,
H.
,
Fukagata
,
K.
, and
Hoepffner
,
J.
,
2010
, “
Phase Relationship in Laminar Channel Flow Controlled by Traveling-Wave-Like Blowing or Suction
,”
Phys. Rev. E
,
81
(
4
), p.
046304
.
233.
Kametani
,
Y.
, and
Fukagata
,
K.
,
2011
, “
Direct Numerical Simulation of Spatially Developing Turbulent Boundary Layers With Uniform Blowing or Suction
,”
J. Fluid Mech.
,
681
, pp.
154
172
.
234.
Nakanishi
,
R.
,
Mamori
,
H.
, and
Fukagata
,
K.
,
2012
, “
Relaminarization of Turbulent Channel Flow Using Traveling Wave-Like Wall Deformation
,”
Int. J. Heat Fluid Flow
,
35
, pp.
152
159
.
235.
Kasagi
,
N.
,
Hasegawa
,
Y.
,
Fukagata
,
K.
, and
Iwamoto
,
K.
,
2012
, “
Control of Turbulent Transport: Less Friction and More Heat Transfer
,”
ASME J. Heat Transfer
,
134
(
3
), p.
031009
.
236.
Rathnasingham
,
R.
, and
Breuer
,
K. S.
,
1997
, “
System Identification and Control of a Turbulent Boundary Layer
,”
Phys. Fluids
,
9
(
7
), pp.
1867
1869
.
237.
Rathnasingham
,
R.
, and
Breuer
,
K. S.
,
2003
, “
Active Control of Turbulent Boundary Layers
,”
J. Fluid Mech.
,
495
, pp.
209
233
.
238.
Rowley
,
C. W.
,
2002
, “
Modeling, Simulation, and Control of Cavity Flow Oscillations
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
239.
Cattafesta
,
L.
,
Shukla
,
D.
,
Garg
,
S.
, and
Ross
,
J.
,
1999
, “
Development of an Adaptive Weapons-Bay Suppression System
,”
AIAA
Paper No. 1999-1901.
240.
Cattafesta
,
L.
,
Williams
,
D.
,
Rowley
,
C.
, and
Alvi
,
F.
,
2003
, “
Review of Active Control of Flow-Induced Cavity Resonance
,”
AIAA
Paper No. 2003-3567.
241.
Cattafesta
,
L. N.
, III
,
Song
,
Q.
,
Williams
,
D. R.
,
Rowley
,
C. W.
, and
Alvi
,
F. S.
,
2008
, “
Active Control of Flow-Induced Cavity Oscillations
,”
Prog. Aerosp. Sci.
,
44
(
7
), pp.
479
502
.
242.
Rowley
,
C. W.
,
Colonius
,
T.
, and
Basu
,
A. J.
,
2002
, “
On Self-Sustained Oscillations in Two-Dimensional Compressible Flow Over Rectangular Cavities
,”
J. Fluid Mech.
,
455
, pp.
315
346
.
243.
Rowley
,
C. W.
,
Colonius
,
T.
, and
Murray
,
R. M.
,
2000
, “
POD Based Models of Self-Sustained Oscillations in the Flow Past an Open Cavity
,”
AIAA
Paper No. 2000-1969.
244.
Rowley
,
C.
,
Colonius
,
T.
, and
Murray
,
R.
,
2004
, “
Model Reduction for Compressible Flows Using POD and Galerkin Projection
,”
Physica D
,
189
(
1–2
), pp.
115
129
.
245.
Rowley
,
C. W.
,
Williams
,
D. R.
,
Colonius
,
T.
,
Murray
,
R. M.
,
MacMartin
,
D. G.
, and
Fabris
,
D.
,
2002
, “
Model-Based Control of Cavity Oscillations. Part II: System Identification and Analysis
,”
AIAA
Paper No. 2002-0972.
246.
Samimy
,
M.
,
Debiasi
,
M.
,
Caraballo
,
E.
,
Malone
,
J.
,
Little
,
J.
,
Özbay
,
H.
,
Efe
,
M.
,
Yan
,
X.
,
Yuan
,
X.
,
DeBonis
,
J.
,
Myatt
,
J.
, and
Camphouse
,
R.
,
2004
, “
Exploring Strategies for Closed-Loop Cavity Flow Control
,”
AIAA
Paper No. 2004-0576.
247.
Rowley
,
C. W.
,
Williams
,
D. R.
,
Colonius
,
T.
,
Murray
,
R. M.
, and
Macmynowski
,
D. G.
,
2006
, “
Linear Models for Control of Cavity Flow Oscillations
,”
J. Fluid Mech.
,
547
, pp.
317
330
.
248.
Samimy
,
M.
,
Debiasi
,
M.
,
Caraballo
,
E.
,
Serrani
,
A.
,
Yuan
,
X.
, and
Little
,
J.
,
2007
, “
Reduced-Order Model-Based Feedback Control of Subsonic Cavity Flows—An Experimental Approach
,”
Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM)
, Vol.
25
,
Springer
,
Berlin
, pp.
211
230
.
249.
Efe
,
M.
,
Debiasi
,
M.
,
Yan
,
P.
,
Özbay
,
H.
, and
Samimy
,
M.
,
2005
, “
Control of Subsonic Cavity Flows by Neural Networks—Analytical Models and Experimental Validation
,”
AIAA
Paper No. 2005-294.
250.
Belson
,
B. A.
,
Semeraro
,
O.
,
Rowley
,
C. W.
, and
Henningson
,
D. S.
,
2013
, “
Feedback Control of Instabilities in the Two-Dimensional Blasius Boundary Layer: The Role of Sensors and Actuators
,”
Phys. Fluids
,
25
(
5
), p.
054106
.
251.
Hervé
,
A.
,
Sipp
,
D.
,
Schmid
,
P. J.
, and
Samuelides
,
M.
,
2012
, “
A Physics-Based Approach to Flow Control Using System Identification
,”
J. Fluid Mech.
,
702
, pp.
26
58
.
252.
Semeraro
,
O.
,
Pralits
,
J. O.
,
Rowley
,
C. W.
, and
Henningson
,
D. S.
,
2013
, “
Riccati-Less Approach for Optimal Control and Estimation: An Application to Two-Dimensional Boundary Layers
,”
J. Fluid Mech.
,
731
, pp.
394
417
.
253.
Weller
,
J.
,
Camarri
,
S.
, and
Iollo
,
A.
,
2009
, “
Feedback Control by Low-Order Modelling of the Laminar Flow Past a Bluff Body
,”
J. Fluid Mech.
,
634
, pp.
405
418
.
254.
Stuart
,
J.
,
1958
, “
On the Non-Linear Mechanics of Hydrodynamic Stability
,”
J. Fluid Mech.
,
4
(
1
), pp.
1
21
.
255.
Stuart
,
J.
,
1971
, “
Nonlinear Stability Theory
,”
Annu. Rev. Fluid Mech.
,
3
, pp.
347
370
.
256.
Schumm
,
M.
,
Berger
,
E.
, and
Monkewitz
,
P.
,
1994
, “
Self-Excited Oscillations in the Wake of Two-Dimensional Bluff Bodies and Their Control
,”
J. Fluid Mech.
,
271
, pp.
17
53
.
257.
Dusek
,
J.
,
Le Gal
,
P.
, and
Fraunié
,
P.
,
1994
, “
A Numerical and Theoretical Study of the First Hopf Bifurcation in a Cylinder Wake
,”
J. Fluid Mech.
,
264
, pp.
59
80
.
258.
Bourgeois
,
J. A.
,
Martinuzzi
,
R. J.
, and
Noack
,
B. R.
,
2013
, “
Generalised Phase Average With Applications to Sensor-Based Flow Estimation of the Wall-Mounted Square Cylinder Wake
,”
J. Fluid Mech.
,
736
, pp.
316
350
.
259.
Luchtenburg, M.,
Tadmor
,
G.
,
Lehmann
,
O.
,
Noack
,
B. R.
,
King
,
R.
, and
Morzyński
,
M.
,
2006
, “
Tuned POD Galerkin Models for Transient Feedback Regulation of the Cylinder Wake
,” 44th AIAA Aerospace Sciences Meeting, Reno, NV, Jan. 9–12,
AIAA
Paper 2006-1407.
260.
Tadmor
,
G.
,
Lehmann
,
O.
,
Noack
,
B. R.
,
Cordier
,
L.
,
Delville
,
J.
,
Bonnet
,
J.-P.
, and
Morzyński
,
M.
,
2011
, “
Reduced Order Models for Closed-Loop Wake Control
,”
Philos. Trans. R. Soc. A
,
369
(
1940
), pp.
1513
1523
.
261.
King
,
R.
,
Seibold
,
M.
,
Lehmann
,
O.
,
Noack
,
B. R.
,
Morzyński
,
M.
, and
Tadmor
,
G.
,
2005
, “
Nonlinear Flow Control Based on a Low Dimensional Model of Fluid Flow
,”
Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems
(Lecture Notes in Control and Information Sciences, Vol. 322),
T.
Meurer
,
K.
Graichen
, and
E.
Gilles
, eds.,
Springer
,
Berlin
, pp.
369
386
.
262.
Bergmann
,
M.
, and
Cordier
,
L.
,
2008
, “
Optimal Control of the Cylinder Wake in the Laminar Regime by Trust-Region Methods and POD Reduced Order Models
,”
J. Comput. Phys.
,
227
(
16
), pp.
7813
7840
.
263.
Parezanovic
,
V.
,
Laurentie
,
J.-C.
,
Duriez
,
T.
,
Fourment
,
C.
,
Delville
,
J.
,
Bonnet
,
J.-P.
,
Cordier
,
L.
,
Noack
,
B. R.
,
Segond
,
M.
,
Abel
,
M.
,
Shaqarin
,
T.
, and
Brunton
,
S. L.
,
2015
, “
Mixing Layer Manipulation Experiment—From Periodic Forcing to Machine Learning Closed-Loop Control
,”
J. Flow Turbul. Combust.
,
94
(
1
), pp.
155
173
.
264.
Aleksic
,
K.
,
Luchtenburg
,
D. M.
,
King
,
R.
,
Noack
,
B. R.
, and
Pfeiffer
,
J.
,
2010
, “
Robust Nonlinear Control Versus Linear Model Predictive Control of a Bluff Body Wake
,”
AIAA
Paper No. 2010-4833.
265.
Duriez
,
T.
,
Parezanovic
,
V.
,
Laurentie
,
J.-C.
,
Fourment
,
C.
,
Delville
,
J.
,
Bonnet
,
J.-P.
,
Cordier
,
L.
,
Noack
,
B. R.
,
Segond
,
M.
,
Abel
,
M.
,
Gautier
,
N.
,
Aider
,
J.-L.
,
Raibaudo
,
C.
,
Cuvier
,
C.
,
Stanislas
,
M.
, and
Brunton
,
S. L.
,
2014
, “
Closed-Loop Control of Experimental Shear Flows Using Machine Learning
,”
AIAA
Paper No. 2014-2219.
266.
Luchtenburg
,
D. M.
,
Schlegel
,
M.
,
Noack
,
B. R.
,
Aleksić
,
K.
,
King
,
R.
,
Tadmor
,
G.
, and
Günther
,
B.
,
2010
, “
Turbulence Control Based on Reduced-Order Models and Nonlinear Control Design
,”
Active Flow Control II
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol.
108
),
R.
King
, ed.,
Springer-Verlag
,
Berlin
, pp.
341
356
.
267.
Farazmand
,
M. M.
,
Kevlahan
,
N. K.-R.
, and
Protas
,
B.
,
2011
, “
Controlling the Dual Cascade of Two-Dimensional Turbulence
,”
J. Fluid Mech.
,
668
, pp.
202
222
.
268.
Schlegel
,
M.
,
Noack
,
B. R.
,
Comte
,
P.
,
Kolomenskiy
,
D.
,
Schneider
,
K.
,
Farge
,
M.
,
Scouten
,
J.
,
Luchtenburg
,
D. M.
, and
Tadmor
,
G.
,
2009
, “
Reduced-Order Modelling of Turbulent Jets for Noise Control
,”
Numerical Simulation of Turbulent Flows and Noise Generation: Results of the DFG/CNRS Research Groups FOR 507 and FOR 508
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM)),
Springer-Verlag
,
Berlin
, pp.
3
27
.
269.
John
,
C.
,
Noack
,
B. R.
,
Schlegel
,
M.
,
Tröltzsch
,
F.
, and
Wachsmuth
,
D.
,
2010
, “
Optimal Boundary Control Problems Related to High-Lift Configurations
,”
Active Flow Control II
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design),
R.
King
, ed.,
Springer-Verlag
,
Berlin
.
270.
Cordier
,
L.
,
Noack
,
B. R.
,
Daviller
,
G.
,
Delvile
,
J.
,
Lehnasch
,
G.
,
Tissot
,
G.
,
Balajewicz
,
M.
, and
Niven
,
R.
,
2013
, “
Control-Oriented Model Identification Strategy
,”
Exp. Fluids
,
54
, p.
1580
.
271.
Noack
,
B. R.
,
Morzyński
,
M.
, and
Tadmor
,
G. E.
,
2011
,
Reduced-Order Modelling for Flow Control
(CISM Courses and Lectures, Vol. 528),
Springer-Verlag
,
Berlin
.
272.
Morzyński
,
M.
,
Stankiewicz
,
W.
,
Noack
,
B. R.
,
Thiele
,
F.
, and
Tadmor
,
G.
,
2006
, “
Generalized Mean-Field Model for Flow Control Using Continuous Mode Interpolation
,”
AIAA
Paper No. 2006-3488.
273.
Sapsis
,
T. P.
, and
Majda
,
A.
,
2013
, “
Statistically Accurate Low-Order Models for Uncertainty Quantification in Turbulent Dynamical Systems
,”
Proc. Natl. Acad. Sci.
,
110
(
34
), pp.
13705
13710
.
274.
Mitchell
,
T. M.
,
1997
,
Machine Learning
,
McGraw-Hill
,
Maidenhead, UK
.
275.
Duda
,
R. O.
,
Hart
,
P. E.
, and
Stork
,
D. G.
,
2000
,
Pattern Classification
,
Wiley-Interscience
,
New York
.
276.
Bishop
,
C. M.
,
2006
,
Pattern Recognition and Machine Learning
, Vol.
1
,
Springer
,
New York
.
277.
Murphy
,
K. P.
,
2012
,
Machine Learning: A Probabilistic Perspective
,
MIT Press
,
Cambridge, MA
.
278.
Fleming
,
P. J.
, and
Purshouse
,
R. C.
,
2002
, “
Evolutionary Algorithms in Control Systems Engineering: A Survey
,”
Control Eng. Pract.
,
10
(
11
), pp.
1223
1241
.
279.
Krstić
,
M.
, and
Wang
,
H.
,
2000
, “
Stability of Extremum Seeking Feedback for General Nonlinear Dynamic Systems
,”
Automatica
,
36
(
4
), pp.
595
601
.
280.
Ariyur
,
K. B.
, and
Krstić
,
M.
,
2003
,
Real-Time Optimization by Extremum-Seeking Control
,
Wiley
,
Hoboken, NJ
.
281.
Beaudoin
,
J.
,
Cadot
,
O.
,
Aider
,
J.
, and
Wesfreid
,
J. E.
,
2006
, “
Bluff-Body Drag Reduction by Extremum-Seeking Control
,”
J. Fluids Struct.
,
22
(
6
), pp.
973
978
.
282.
Beaudoin
,
J.-F.
,
Cadot
,
O.
,
Aider
,
J.-L.
, and
Wesfreid
,
J.-E.
,
2006
, “
Drag Reduction of a Bluff Body Using Adaptive Control Methods
,”
Phys. Fluids
,
18
(
8
), p.
085107
.
283.
Becker
,
R.
,
King
,
R.
,
Petz
,
R.
, and
Nitsche
,
W.
,
2007
, “
Adaptive Closed-Loop Control on a High-Lift Configuration Using Extremum Seeking
,”
AIAA J.
,
45
(
6
), pp.
1382
1392
.
284.
Banaszuk
,
A.
,
Zhang
,
Y.
, and
Jacobson
,
C. A.
,
2000
, “
Adaptive Control of Combustion Instability Using Extremum-Seeking
,”
American Control Conference
(
ACC
), Chicago, June 28–30, Vol.
1
, pp.
416
422
.
285.
Banaszuk
,
A.
,
Ariyur
,
K. B.
,
Krstić
,
M.
, and
Jacobson
,
C. A.
,
2004
, “
An Adaptive Algorithm for Control of Combustion Instability
,”
Automatica
,
40
(
11
), pp.
1965
1972
.
286.
Banaszuk
,
A.
,
Narayanan
,
S.
, and
Zhang
,
Y.
,
2003
, “
Adaptive Control of Flow Separation in a Planar Diffuser
,”
AIAA
Paper No. 2003-617.
287.
Maury
,
R.
,
Keonig
,
M.
,
Cattafesta
,
L.
,
Jordan
,
P.
, and
Delville
,
J.
,
2012
, “
Extremum-Seeking Control of Jet Noise
,”
Aeroacoustics
,
11
(
3–4
), pp.
459
474
.
288.
Gelbert
,
G.
,
Moeck
,
J. P.
,
Paschereit
,
C. O.
, and
King
,
R.
,
2012
, “
Advanced Algorithms for Gradient Estimation in One- and Two-Parameter Extremum Seeking Controllers
,”
J. Process Control
,
22
(
4
), pp.
700
709
.
289.
Wiederhold
,
O.
,
King
,
R.
,
Noack
,
B. R.
,
Neuhaus
,
L.
,
Neise
,
W.
,
Enghard
,
L.
, and
Swoboda
,
M.
,
2009
, “
Extensions of Extremum-Seeking Control to Improve the Aerodynamic Performance of Axial Turbomachines
,”
AIAA
Paper No. 092407.
290.
Krieger
,
J. P.
, and
Krstić
,
M.
,
2011
, “
Extremum Seeking Based on Atmospheric Turbulence for Aircraft Endurance
,”
J. Guid. Control Dyn.
,
34
(
6
), pp.
1876
1885
.
291.
Killingsworth
,
N. J.
, and
Krstić
,
M.
,
2006
, “
PID Tuning Using Extremum Seeking: Online, Model-Free Performance Optimization
,”
IEEE Control Syst. Mag.
,
26
(
1
), pp.
70
79
.
292.
Krstić
,
M.
,
Krupadanam
,
A.
, and
Jacobson
,
C.
,
1999
, “
Self-Tuning Control of a Nonlinear Model of Combustion Instabilities
,”
IEEE Trans. Control Syst. Technol.
,
7
(
4
), pp.
424
436
.
293.
Koumoutsakos
,
P.
,
1997
, “
Active Control of Turbulent Channel Flow
,”
Center for Turbulence Research
, Stanford University, Stanford, CA, Annual Research Briefs, C, pp. 289–297.
294.
Pamiès
,
M.
,
Garnier
,
E.
,
Merlen
,
A.
, and
Sagaut
,
P.
,
2007
, “
Response of a Spatially Developing Turbulent Boundary Layer to Active Control Strategies in the Framework of Opposition Control
,”
Phys. Fluids
,
19
(
10
), p.
108102
.
295.
Iwamoto
,
K.
,
Fukagata
,
K.
,
Kasagi
,
N.
, and
Suzuki
,
Y.
,
2005
, “
Friction Drag Reduction Achievable by Near-Wall Turbulence Manipulation at High Reynolds Numbers
,”
Phys. Fluids
,
17
(
1
), p.
011702
.
296.
Chung
,
Y. M.
, and
Talha
,
T.
,
2011
, “
Effectiveness of Active Flow Control for Turbulent Skin Friction Drag Reduction
,”
Phys. Fluids
,
23
(
2
), p.
025102
.
297.
Rebbeck
,
H.
, and
Choi
,
K.-S.
,
2001
, “
Opposition Control of Near-Wall Turbulence With a Piston-Type Actuator
,”
Phys. Fluids
,
13
(
8
), pp.
2142
2145
.
298.
Endo
,
T.
,
Kasagi
,
N.
, and
Suzuki
,
Y.
,
2000
, “
Feedback Control of Wall Turbulence With Wall Deformation
,”
Int. J. Heat Fluid Flow
,
21
(
5
), pp.
568
575
.
299.
Fukagata
,
K.
, and
Kasagi
,
N.
,
2002
, “
Active Control for Drag Reduction in Turbulent Pipe Flow
,” Engineering Turbulence Modelling and Experiments 5,
W.
Rodi
and
N.
Fueyo
, eds., Elsevier Science, Oxford, UK, pp. 607–616.
300.
Fukagata
,
K.
, and
Kasagi
,
N.
,
2003
, “
Drag Reduction in Turbulent Pipe Flow With Feedback Control Applied Partially to Wall
,”
Int. J. Heat Fluid Flow
,
24
(
4
), pp.
480
490
.
301.
Fukagata
,
K.
, and
Kasagi
,
N.
,
2004
, “
Suboptimal Control for Drag Reduction Via Suppression of Near-Wall Reynolds Shear Stress
,”
Int. J. Heat Fluid Flow
,
25
(
3
), pp.
341
350
.
302.
Farrell
,
B. F.
, and
Ioannou
,
P. J.
,
1996
, “
Turbulence Suppression by Active Control
,”
Phys. Fluids
,
8
(
5
), pp.
1257
1268
.
303.
Luhar
,
M.
,
Sharma
,
A. S.
, and
McKeon
,
B. J.
,
2014
, “
Opposition Control Within the Resolvent Analysis Framework
,”
J. Fluid Mech.
,
749
, pp.
597
626
.
304.
Cheng
,
B.
, and
Titterington
,
D. M.
,
1994
, “
Neural Networks: A Review From a Statistical Perspective
,”
Statistical Science
,
9
(
1
), pp.
2
30
.
305.
Haykin
,
S.
,
2004
,
Neural Networks: A Comprehensive Foundation
,
Prentice Hall
,
Upper Saddle River, NJ
.
306.
Müller
,
S.
,
Milano
,
M.
, and
Koumoutsakos
,
P.
,
1999
, “
Application of Machine Learning Algorithms to Flow Modeling and Optimization
,”
Center for Turbulence Research Annual Research Briefs
, Stanford University, Stanford, CA, pp.
169
178
.
307.
Milano
,
M.
, and
Koumoutsakos
,
P.
,
2002
, “
Neural Network Modeling for Near Wall Turbulent Flow
,”
J. Comput. Phys.
,
182
(
1
), pp.
1
26
.
308.
Oja
,
E.
,
1992
, “
Principal Components, Minor Components, and Linear Neural Networks
,”
Neural Networks
,
5
(
6
), pp.
927
935
.
309.
Oja
,
E.
,
1997
, “
The Nonlinear PCA Learning Rule in Independent Component Analysis
,”
Neurocomputing
,
17
(
1
), pp.
25
45
.
310.
Karhunen
,
J.
, and
Joutsensalo
,
J.
,
1994
, “
Representation and Separation of Signals Using Nonlinear PCA Type Learning
,”
Neural Networks
,
7
(
1
), pp.
113
127
.
311.
Nair
,
A. G.
, and
Taira
,
K.
,
2015
, “
Network-Theoretic Approach to Sparsified Discrete Vortex Dynamics
,”
J. Fluid Mech.
,
768
, pp.
549
571
.
312.
Ciresan
,
D.
,
Meier
,
U.
, and
Schmidhuber
,
J.
,
2012
, “
Multi-Column Deep Neural Networks for Image Classification
,”
IEEE Conference on Computer Vision and Pattern Recognition
(
CVPR
), Providence, RI, June 16–21, pp.
3642
3649
.
313.
Dean
,
J.
,
Corrado
,
G.
,
Monga
,
R.
,
Chen
,
K.
,
Devin
,
M.
,
Mao
,
M.
,
Senior
,
A.
,
Tucker
,
P.
,
Yang
,
K.
,
Le
,
Q. V.
, and
Ng
,
A. Y.
,
2012
, “
Large Scale Distributed Deep Networks
,”
Advances in Neural Information Processing Systems 25
,
F.
Pereira
,
C. J. C.
Burges
,
L.
Bottou
, and
K. Q.
Weinberger
, eds., Curran Associates, Inc., Red Hook, NY. pp.
1223
1231
.
314.
Hinton
,
G.
,
Deng
,
L.
,
Yu
,
D.
,
Dahl
,
G. E.
,
Mohamed
,
A.-R.
,
Jaitly
,
N.
,
Senior
,
A.
,
Vanhoucke
,
V.
,
Nguyen
,
P.
,
Sainath
,
T. N.
, and
Kingsbury
,
B.
,
2012
, “
Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups
,”
Signal Process. Mag.
,
29
(
6
), pp.
82
97
.
315.
Holland
,
J. H.
,
1975
,
Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence
,
University of Michigan Press
, Ann Arbor, MI.
316.
Davis
,
L.
,
1991
,
Handbook of Genetic Algorithms
, Vol.
115
,
Van Nostrand Reinhold
,
New York
.
317.
Goldberg
,
D. E.
,
2006
,
Genetic Algorithms
,
Pearson Education India
, Delhi, India.
318.
Koza
,
J. R.
,
1992
,
Genetic Programming: On the Programming of Computers by Means of Natural Selection
, Vol.
1
,
MIT Press
,
Cambridge, MA
.
319.
Koza
,
J. R.
,
Bennet
,
F. H.
, III
, and
Stiffelman
,
O.
,
1999
, “
Genetic Programming as a Darwinian Invention Machine
,”
Genetic Programming
,
Springer
, Berlin, pp.
93
108
.
320.
Koumoutsakos
,
P.
,
Freund
,
J.
, and
Parekh
,
D.
,
2001
, “
Evolution Strategies for Automatic Optimization of Jet Mixing
,”
AIAA J.
,
39
(
5
), pp.
967
969
.
321.
Buche
,
D.
,
Stoll
,
P.
,
Dornberger
,
R.
, and
Koumoutsakos
,
P.
,
2002
, “
Multiobjective Evolutionary Algorithm for the Optimization of Noisy Combustion Processes
,”
IEEE Trans. Systems, Man, and Cybernet., Part C
,
32
(
4
), pp.
460
473
.
322.
Poncet
,
P.
,
Cottet
,
G.-H.
, and
Koumoutsakos
,
P.
,
2005
, “
Control of Three-Dimensional Wakes Using Evolution Strategies
,”
C. R. Mec.
,
333
(
1
), pp.
65
77
.
323.
Fukagata
,
K.
,
Kern
,
S.
,
Chatelain
,
P.
,
Koumoutsakos
,
P.
, and
Kasagi
,
N.
,
2008
, “
Evolutionary Optimization of an Anisotropic Compliant Surface for Turbulent Friction Drag Reduction
,”
J. Turbul.
,
9
(
35
), pp.
1
17
.
324.
Gazzola
,
M.
,
Vasilyev
,
O. V.
, and
Koumoutsakos
,
P.
,
2011
, “
Shape Optimization for Drag Reduction in Linked Bodies Using Evolution Strategies
,”
Comput. Struct.
,
89
(
11
), pp.
1224
1231
.
325.
Hansen
,
N.
,
Niederberger
,
A. S.
,
Guzzella
,
L.
, and
Koumoutsakos
,
P.
,
2009
, “
A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion
,”
IEEE Trans. Evol. Comput.
,
13
(
1
), pp.
180
197
.
326.
Noack
,
B. R.
,
Duriez
,
T.
,
Cordier
,
L.
,
Segond
,
M.
,
Abel
,
M.
,
Brunton
,
S. L.
,
Morzyński
,
M.
,
Laurentie
,
J.-C.
,
Parezanovic
,
V.
, and
Bonnet
,
J.-P.
,
2013
, “
Closed-Loop Turbulence Control With Machine Learning Methods
,”
Bull. Am. Phys. Soc.
,
58
(
18
), p.
418
.
327.
Parezanović
,
V.
,
Duriez
,
T.
,
Cordier
,
L.
,
Noack
,
B. R.
,
Delville
,
J.
,
Bonnet
,
J.-P.
,
Segond
,
M.
,
Abel
,
M.
, and
Brunton
,
S. L.
,
2014
, “
Closed-Loop Control of an Experimental Mixing Layer Using Machine Learning Control
,” preprint
arXiv:1408.3259
.
328.
Gautier
,
N.
,
Aider
,
J.-L.
,
Duriez
,
T.
,
Noack
,
B. R.
,
Segond
,
M.
, and
Abel
,
M.
,
2015
, “
Closed-Loop Separation Control Using Machine Learning
,”
J. Fluid Mech.
,
770
, pp.
442
457
.
329.
Duriez
,
T.
,
Parezanović
,
V.
,
Cordier
,
L.
,
Noack
,
B. R.
,
Delville
,
J.
,
Bonnet
,
J.-P.
,
Segond
,
M.
, and
Abel
,
M.
,
2014
, “
Closed-Loop Turbulence Control Using Machine Learning
,” preprint
arXiv:1404.4589
.
330.
Gautier
,
N.
,
2014
, “
Flow Control Using Optical Sensors
,” Ph.D. thesis, Ecole Doctorale: Sciences Mécaniques, Acoustique, Électronique & Robotique (UPMC), ESPCI, Laboratoire PMMH, Paris.
331.
Gunzburger
,
M. D.
,
2003
,
Perspectives in Flow Control and Optimization
, Vol.
5
,
SIAM
,
Philadelphia
.
332.
Williams
,
D.
, and
MacMynowski
,
D.
, “
Brief History of Flow Control
,”
Fundamentals and Applications of Modern Flow Control
, Vol.
231
,
R.
Joslin
and
D.
Miller
, eds., American Institute of Aeronautics and Astronautics, Reston, VA, pp.
1
20
.
333.
Schlichting
,
H.
,
1979
,
Boundary-Layer Theory
, 7th ed.,
McGraw-Hill
,
New York
.
334.
Fiedler
,
H.
, and
Fernholz
,
H.-H.
,
1990
, “
On the Management and Control of Turbulent Shear Flows
,”
Prog. Aeronaut. Sci.
,
27
(
4
), pp.
305
387
.
335.
McComb
,
D.
,
1991
,
The Physics of Fluid Turbulence
, 1st ed.,
Clarendon Press
,
Oxford, UK
.
336.
Frisch
,
U.
,
1995
,
Turbulence
, 1st ed.,
Cambridge University Press
,
Cambridge, UK
.
337.
Taylor
,
H.
,
1947
, “
The Elimination of Diffuser Separation by Vortex Generators
,” United Aircraft Corporation, East Hartford, CT, Technical Report No. R.4012-3.
338.
Lorenz
,
E. N.
,
1963
, “
Deterministic Nonperiodic Flow
,”
J. Atmos. Sci.
,
20
(
2
), pp.
130
141
.
339.
Ott
,
E.
,
Grebogi
,
C.
, and
Yorke
,
J. A.
,
1990
, “
Controlling Chaos
,”
Phys. Rev. Lett.
,
64
(
23
), p.
2837
.
340.
Schöll
,
E.
, and
Schuster
,
H. G.
,
2007
,
Handbook of Chaos Control
,
Wiley-VCH
,
Weinheim, Germany
.
341.
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
,
1988
, “
The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
192
, pp.
115
173
.
342.
Glauser
,
M. N.
,
Leib
,
S. J.
, and
George
,
W. K.
,
1987
,
Coherent Structures in the Axisymmetric Turbulent Jet Mixing Layer
,
Springer
,
Berlin
.
343.
George
,
W. K.
,
1988
, “
Insight Into the Dynamics of Coherent Structures From a Proper Orthogonal Decomposition
,” Symposium on Near Wall Turbulence, Dubrovnik, Yugoslavia, May 16–20.
344.
Glauser
,
M. N.
, and
George
,
W. K.
,
1992
, “
Application of Multipoint Measurements for Flow Characterization
,”
Exp. Therm. Fluid Sci.
,
5
(
5
), pp.
617
632
.
345.
Guyot
,
D.
,
Paschereit
,
C. O.
, and
Raghu
,
S.
,
2009
, “
Active Combustion Control Using a Fluidic Oscillator for Asymmetric Fuel Flow Modulation
,”
Int. J. Flow Control
,
1
(
2
), pp.
155
166
.
346.
Bobusch
,
B. C.
,
Woszidlo
,
R.
,
Bergada
,
J.
,
Nayeri
,
C. N.
, and
Paschereit
,
C. O.
,
2013
, “
Experimental Study of the Internal Flow Structures Inside a Fluidic Oscillator
,”
Exp. Fluids
,
54
(
6
), p.
1559
.
347.
Vallikivi
,
M.
,
Hultmark
,
M.
,
Bailey
,
S.
, and
Smits
,
A.
,
2011
, “
Turbulence Measurements in Pipe Flow Using a Nano-Scale Thermal Anemometry Probe
,”
Exp. Fluids
,
51
(
6
), pp.
1521
1527
.
348.
Bailey
,
S. C.
,
Kunkel
,
G. J.
,
Hultmark
,
M.
,
Vallikivi
,
M.
,
Hill
,
J. P.
,
Meyer
,
K. A.
,
Tsay
,
C.
,
Arnold
,
C. B.
, and
Smits
,
A. J.
,
2010
, “
Turbulence Measurements Using a Nanoscale Thermal Anemometry Probe
,”
J. Fluid Mech.
,
663
, pp.
160
179
.
349.
Hultmark
,
M.
,
Vallikivi
,
M.
,
Bailey
,
S.
, and
Smits
,
A.
,
2012
, “
Turbulent Pipe Flow at Extreme Reynolds Numbers
,”
Phys. Rev. Lett.
,
108
(
9
), p.
094501
.
350.
Daniel
,
T. L.
,
1988
, “
Forward Flapping Flight From Flexible Fins
,”
Can. J. Zool.
,
66
(
3
), pp.
630
638
.
351.
Anderson
,
J. M.
,
Streitlien
,
K.
,
Barrett
,
D. S.
, and
Triantafyllou
,
M. S.
,
1998
, “
Oscillating Foils of High Propulsive Efficiency
,”
J. Fluid Mech.
,
360
, pp.
41
72
.
352.
Triantafyllou
,
M. S.
, and
Triantafyllou
,
G. S.
,
1995
, “
An Efficient Swimming Machine
,”
Sci. Am.
,
272
(
3
), pp.
64
71
.
353.
Allen
,
J. J.
, and
Smits
,
A. J.
, “
Energy Harvesting Eel
,”
J. Fluids Struct.
,
15
(
3–4
), pp.
629
640
.
354.
Combes
,
S. A.
, and
Daniel
,
T. L.
,
2001
, “
Shape, Flapping and Flexion: Wing and Fin Design for Forward Flight
,”
J. Exp. Biol.
,
204
(
12
), pp.
2073
2085
.
355.
Clark
,
R. P.
, and
Smits
,
A. J.
,
2006
, “
Thrust Production and Wake Structure of a Batoid-Inspired Oscillating Fin
,”
J. Fluid Mech.
,
562
, pp.
415
429
.
356.
Buchholz
,
J. H.
, and
Smits
,
A. J.
,
2008
, “
The Wake Structure and Thrust Performance of a Rigid Low-Aspect-Ratio Pitching Panel
,”
J. Fluid Mech.
,
603
(May), pp.
331
365
.
357.
Song
,
A.
,
Tian
,
X.
,
Israeli
,
E.
,
Galvao
,
R.
,
Bishop
,
K.
,
Swartz
,
S.
, and
Breuer
,
K.
,
2008
, “
Aeromechanics of Membrane Wings With Implications for Animal Flight
,”
AIAA J.
,
46
(
8
), pp.
2096
2106
.
358.
Taira
,
K.
, and
Colonius
,
T.
,
2008
, “
Effect of Tip Vortices in Low-Reynolds-Number Poststall Flow Control
,”
AIAA J.
,
47
(
3
), pp.
749
756
.
359.
Taira
,
K.
, and
Colonius
,
T.
,
2009
, “
Three-Dimensional Flows Around Low-Aspect-Ratio Flat-Plate Wings at Low Reynolds Numbers
,”
J. Fluid Mech.
,
623
, pp.
187
207
.
360.
Whittlesey
,
R. W.
,
Liska
,
S. C.
, and
Dabiri
,
J. O.
,
2010
, “
Fish Schooling as a Basis for Vertical-Axis Wind Turbine Farm Design
,”
Bioinspiration Biomimetics
,
5
(
3
), p.
035005
.
361.
Faruque
,
I.
, and
Humbert
,
J. S.
,
2010
, “
Dipteran Insect Flight Dynamics. Part 1: Longitudinal Motion About Hover
,”
J. Theor. Biol.
,
264
(
2
), pp.
538
552
.
362.
Faruque
,
I.
, and
Humbert
,
J. S.
,
2010
, “
Dipteran Insect Flight Dynamics. Part 2: Lateral–Directional Motion About Hover
,”
J. Theor. Biol.
,
265
(
3
), pp.
306
313
.
363.
Humbert
,
J. S.
, and
Hyslop
,
A. M.
,
2010
, “
Bioinspired Visuomotor Convergence
,”
IEEE Trans. Rob.
,
26
(
1
), pp.
121
130
.
364.
Shelley
,
M. J.
, and
Zhang
,
J.
,
2011
, “
Flapping and Bending Bodies Interacting With Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
43
, pp.
449
465
.
365.
Leftwich
,
M. C.
,
Tytell
,
E. D.
,
Cohen
,
A. H.
, and
Smits
,
A. J.
,
2012
, “
Wake Structures Behind a Swimming Robotic Lamprey With a Passively Flexible Tail
,”
J. Exp. Biol.
,
215
(
3
), pp.
416
425
.
366.
Dewey
,
P. A.
,
Carriou
,
A.
, and
Smits
,
A. J.
,
2012
, “
On the Relationship Between Efficiency and Wake Structure of a Batoid-Inspired Oscillating Fin
,”
J. Fluid Mech.
,
691
, pp.
245
266
.
367.
Nawroth
,
J. C.
,
Lee
,
H.
,
Feinberg
,
A. W.
,
Ripplinger
,
C. M.
,
McCain
,
M. L.
,
Grosberg
,
A.
,
Dabiri
,
J. O.
, and
Parker
,
K. K.
,
2012
, “
A Tissue-Engineered Jellyfish With Biomimetic Propulsion
,”
Nat. Biotechnol.
,
30
, pp.
792
797
.
368.
Roth
,
E.
,
Sponberg
,
S.
, and
Cowan
,
N.
,
2014
, “
A Comparative Approach to Closed-Loop Computation
,”
Curr. Opin. Neurobiol.
,
25
, pp.
54
62
.
369.
Cowan
,
N. J.
,
Ankarali
,
M. M.
,
Dyhr
,
J. P.
,
Madhav
,
M. S.
,
Roth
,
E.
,
Sefati
,
S.
,
Sponberg
,
S.
,
Stamper
,
S. A.
,
Fortune
,
E. S.
, and
Daniel
,
T. L.
,
2014
, “
Feedback Control as a Framework for Understanding Tradeoffs in Biology
,”
Integr. Comp. Biol.
,
54
(
2
), pp.
223
237
.
370.
Dickinson
,
M. H.
, and
Gotz
,
K. G.
,
1996
, “
The Wake Dynamics and Flight Forces of the Fruit Fly Drosophila melanogaster
,”
J. Exp. Biol.
,
199
(
9
), pp.
2085
2104
.
371.
Sane
,
S. P.
, and
Dickinson
,
M. H.
,
2001
, “
The Control of Flight Force by a Flapping Wing: Lift and Drag Production
,”
J. Exp. Biol.
,
204
(
15
), pp.
2607
2626
.
372.
Frye
,
M. A.
, and
Dickinson
,
M. H.
,
2001
, “
Fly Flight: A Model for the Neural Control of Complex Behavior
,”
Neuron
,
32
(
3
), pp.
385
388
.
373.
Ghose
,
K.
,
Horiuchi
,
T. K.
,
Krishnaprasad
,
P. S.
, and
Moss
,
C. F.
,
2006
, “
Echolocating Bats Use a Nearly Time-Optimal Strategy to Intercept Prey
,”
PLoS Biol.
,
4
(
5
), p.
e108
.
374.
Hedenström
,
A.
,
Johansson
,
L.
,
Wolf
,
M.
,
Von Busse
,
R.
,
Winter
,
Y.
, and
Spedding
,
G.
,
2007
, “
Bat Flight Generates Complex Aerodynamic Tracks
,”
Science
,
316
(
5826
), pp.
894
897
.
375.
Riskin
,
D. K.
,
Willis
,
D. J.
,
Iriarte-Díaz
,
J.
,
Hedrick
,
T. L.
,
Kostandov
,
M.
,
Chen
,
J.
,
Laidlaw
,
D. H.
,
Breuer
,
K. S.
, and
Swartz
,
S. M.
,
2008
, “
Quantifying the Complexity of Bat Wing Kinematics
,”
J. Theor. Biol.
,
254
(
3
), pp.
604
615
.
376.
Hubel
,
T. Y.
,
Hristov
,
N. I.
,
Swartz
,
S. M.
, and
Breuer
,
K. S.
,
2009
, “
Time-Resolved Wake Structure and Kinematics of Bat Flight
,”
Exp. Fluids
,
46
(
5
), pp.
933
943
.
377.
Fish
,
F. E.
, and
Hui
,
C. A.
,
1991
, “
Dolphin Swimming—A Review
,”
Mamm. Rev.
,
21
(
4
), pp.
181
195
.
378.
Fish
,
F. E.
,
1996
, “
Transitions From Drag-Based to Lift-Based Propulsion in Mammalian Swimming
,”
Am. Zool.
,
36
(
6
), pp.
628
641
.
379.
Dickinson
,
M. H.
,
Lehmann
,
F. O.
, and
Sane
,
S. P.
,
1999
, “
Wing Rotation and the Aerodynamic Basis of Insect Flight
,”
Science
,
284
(
5422
), pp.
1954
1960
.
380.
Birch
,
J.
, and
Dickinson
,
M.
,
2001
, “
Spanwise Flow and the Attachment of the Leading-Edge Vortex on Insect Wings
,”
Nature
,
412
(
6848
), pp.
729
733
.
381.
Sane
,
S. P.
,
2003
, “
The Aerodynamics of Insect Flight
,”
J. Exp. Biol.
,
206
(
23
), pp.
4191
4208
.
382.
Liao
,
J. C.
,
Beal
,
D. N.
,
Lauder
,
G. V.
, and
Triantafyllou
,
M. S.
,
2003
, “
Fish Exploiting Vortices Decrease Muscle Activity
,”
Science
,
302
(
5650
), pp.
1566
1569
.
383.
Tytell
,
E. D.
, and
Lauder
,
G. V.
,
2004
, “
The Hydrodynamics of Eel Swimming. I. Wake Structure
,”
J. Exp. Biol.
,
207
(
11
), pp.
1825
1841
.
384.
Lauder
,
G. V.
, and
Tytell
,
E. D.
,
2005
, “
Hydrodynamics of Undulatory Propulsion
,”
Fish Physiol.
,
23
, pp.
425
468
.
385.
Videler
,
J. J.
,
Samhuis
,
E. J.
, and
Povel
,
G. D. E.
,
2004
, “
Leading-Edge Vortex Lifts Swifts
,”
Science
,
306
(
5703
), pp.
1960
1962
.
386.
Wang
,
Z. J.
,
2005
, “
Dissecting Insect Flight
,”
Annu. Rev. Fluid Mech.
,
37
, pp.
183
210
.
387.
Dabiri
,
J. O.
,
2009
, “
Optimal Vortex Formation as a Unifying Principle in Biological Propulsion
,”
Annu. Rev. Fluid Mech.
,
41
, pp.
17
33
.
388.
Wu
,
T. Y.
,
2011
, “
Fish Swimming and Bird/Insect Flight
,”
Annu. Rev. Fluid Mech.
,
43
, pp.
25
58
.
389.
Collett
,
T. S.
, and
Land
,
M. F.
,
1975
, “
Visual Control of Flight Behaviour in the Hoverfly Syritta pipiens L.
,”
J. Comp. Physiol. A
,
99
(
1
), pp.
1
66
.
390.
Fayyazuddin
,
A.
, and
Dickinson
,
M. H.
,
1996
, “
Haltere Afferents Provide Direct, Electronic Input to a Steering Motor Neuron in the Blowfly, Calliphora
,”
J. Neurosci.
,
16
(
16
), pp.
5225
5232
.
391.
Fox
,
J. L.
, and
Daniel
,
T. L.
,
2008
, “
A Neural Basis for Gyroscopic Force Measurement in the Halteres of Holorusia
,”
J. Comp. Physiol. A
,
194
(
10
), pp.
887
897
.
392.
Sane
,
S. P.
,
Dieudonne
,
A.
,
Willis
,
M. A.
, and
Daniel
,
T. L.
,
2007
, “
Antennal Mechanosensors Mediate Flight Control in Moths
,”
Science
,
315
(
5813
), pp.
863
866
.
393.
Brown
,
R. E.
, and
Fedde
,
M. R.
,
1993
, “
Airflow Sensors in the Avian Wing
,”
J. Exp. Biol.
,
179
(
1
), pp.
13
30
.
394.
Sterbing-D'Angelo
,
S. J.
, and
Moss
,
C. F.
,
2014
, “
Air Flow Sensing in Bats
,”
Flow Sensing in Air and Water
,
Springer
,
Berlin
, pp.
197
213
.
395.
Sterbing-D'Angelo
,
S.
,
Chadha
,
M.
,
Chiu
,
C.
,
Falk
,
B.
,
Xian
,
W.
,
Barcelo
,
J.
,
Zook
,
J. M.
, and
Moss
,
C. F.
,
2011
, “
Bat Wing Sensors Support Flight Control
,”
Proc. Natl. Acad. Sci.
,
108
(
27
), pp.
11291
11296
.
396.
Dickinson
,
B.
,
2010
, “
Hair Receptor Sensitivity to Changes in Laminar Boundary Layer Shape
,”
Bioinspiration Biomimetics
,
5
(
1
), p.
016002
.
397.
Massey
,
T.
,
Kapur
,
R.
,
Dabiri
,
F.
,
Vu
,
L. N.
, and
Sarrafzadeh
,
M.
,
2007
, “
Localization Using Low-Resolution Optical Sensors
,”
IEEE International Conference on Mobile Adhoc and Sensor Systems
(
MASS 2007
), Pisa, Italy, Oct. 8–11.
398.
Giannetti
,
F.
, and
Luchini
,
P.
,
2007
, “
Structural Sensitivity of the First Instability of the Cylinder Wake
,”
J. Fluid Mech.
,
581
, pp.
167
197
.
399.
Hof
,
B.
,
de Lozar
,
A.
,
Avila
,
M.
,
Tu
,
X.
, and
Schneider
,
T. M.
,
2010
, “
Eliminating Turbulence in Spatially Intermittent Flows
,”
Science
,
327
(
5972
), pp.
1491
1494
.
400.
McKeon
,
B. J.
,
2010
, “
Controlling Turbulence
,”
Science
,
327
(
5927
), pp.
1462
1463
.
401.
Avila
,
K.
,
Moxey
,
D.
,
de Lozar
,
A.
,
Avila
,
M.
,
Barkley
,
D.
, and
Hof
,
B.
,
2011
, “
The Onset of Turbulence in Pipe Flow
,”
Science
,
333
(
6039
), pp.
192
196
.
402.
Brunton
,
B. W.
,
Brunton
,
S. L.
,
Proctor
,
J. L.
, and
Kutz
,
J. N.
,
2013
, “
Optimal Sensor Placement and Enhanced Sparsity for Classification
,” preprint
arXiv:1310.4217
.
403.
Proctor
,
J. L.
,
Brunton
,
S. L.
,
Brunton
,
B. W.
, and
Kutz
,
J. N.
,
2014
, “
Exploiting Sparsity and Equation-Free Architectures in Complex Systems (Invited Review)
,”
Eur. Phys. J. Spec. Top.
,
223
(
13
), pp.
2665
2684
.
404.
Hey
,
A. J.
,
Tansley
,
S.
, and
Tolle
,
K. M.
,
2009
,
The Fourth Paradigm: Data-Intensive Scientific Discovery
,
Microsoft Research
,
Redmond, WA
.
405.
Allaire
,
D.
,
Biros
,
G.
,
Chambers
,
J.
,
Ghattas
,
O.
,
Kordonowy
,
D.
, and
Willcox
,
K.
,
2012
, “
Dynamic Data Driven Methods for Self-Aware Aerospace Vehicles
,”
Proc. Comput. Sci.
,
9
, pp.
1206
1210
.
406.
Kutz
,
J. N.
,
2013
,
Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data
,
Oxford University Press
, Oxford, UK.
407.
Candès
,
E. J.
,
2006
, “
Compressive Sampling
,”
International Congress of Mathematics
, Madrid, Aug. 22–30, Vol. 3, pp. 1433–1452.
408.
Donoho
,
D. L.
,
2006
, “
Compressed Sensing
,”
IEEE Trans. Inf. Theory
,
52
(
4
), pp.
1289
1306
.
409.
Baraniuk
,
R. G.
,
2007
, “
Compressive Sensing
,”
IEEE Signal Process. Mag.
,
24
(
4
), pp.
118
120
.
410.
Tropp
,
J. A.
, and
Gilbert
,
A. C.
,
2007
, “
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
,”
IEEE Trans. Inf. Theory
,
53
(
12
), pp.
4655
4666
.
411.
Candès
,
E. J.
, and
Wakin
,
M. B.
,
2008
, “
An Introduction to Compressive Sampling
,”
IEEE Signal Process. Mag.
,
25
(
2
), pp.
21
30
.
412.
Willert
,
C. E.
, and
Gharib
,
M.
,
1991
, “
Digital Particle Image Velocimetry
,”
Exp. Fluids
,
10
(
4
), pp.
181
193
.
413.
Nyquist
,
H.
,
1928
, “
Certain Topics in Telegraph Transmission Theory
,”
Trans. AIEE
,
47
(
2
), pp.
617
644
.
414.
Shannon
,
C. E.
,
1948
, “
A Mathematical Theory of Communication
,”
Bell Syst. Tech. J.
,
27
(
3
), pp.
379
423
.
415.
Petra
,
S.
, and
Schnörr
,
C.
,
2009
, “
TomoPIV Meets Compressed Sensing
,”
Pure Math. Appl.
,
20
(
1–2
), pp.
49
76
.
416.
Becker
,
F.
,
Wieneke
,
B.
,
Petra
,
S.
,
Schröder
,
A.
, and
Schnörr
,
C.
,
2012
, “
Variational Adaptive Correlation Method for Flow Estimation
,”
IEEE Trans. Image Process.
,
21
(
6
), pp.
3053
3065
.
417.
Bai
,
Z.
,
Wimalajeewa
,
T.
,
Berger
,
Z.
,
Wang
,
G.
,
Glauser
,
M.
, and
Varshney
,
P. K.
,
2013
, “
Physics Based Compressive Sensing Approach Applied to Airfoil Data Collection and Analysis
,”
AIAA
Paper No. 2013-0772.
418.
Bai
,
Z.
,
Wimalajeewa
,
T.
,
Berger
,
Z.
,
Wang
,
G.
,
Glauser
,
M.
, and
Varshney
,
P. K.
,
2014
, “
Low-Dimensional Approach for Reconstruction of Airfoil Data Via Compressive Sensing
,”
AIAA J.
,
53
(
4
), pp.
920
933
.
419.
Candès
,
E. J.
,
Romberg
,
J.
, and
Tao
,
T.
,
2006
, “
Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information
,”
IEEE Trans. Inf. Theory
,
52
(
2
), pp.
489
509
.
420.
Candès
,
E. J.
,
Romberg
,
J.
, and
Tao
,
T.
,
2006
, “
Stable Signal Recovery From Incomplete and Inaccurate Measurements
,”
Commun. Pure Appl. Math.
,
59
(
8
), pp.
1207
1223
.
421.
Candès
,
E. J.
, and
Tao
,
T.
,
2006
, “
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Trans. Inf. Theory
,
52
(
12
), pp.
5406
5425
.
422.
Boyd
,
S.
, and
Vandenberghe
,
L.
,
2009
,
Convex Optimization
,
Cambridge University Press
, Cambridge, UK.
423.
Mathelin
,
L.
, and
Gallivan
,
K. A.
,
2012
, “
A Compressed Sensing Approach for Partial Differential Equations With Random Input Data
,”
Commun. Comput. Phys.
,
12
(
4
), pp.
1
36
.
424.
Schaeffer
,
H.
,
Caflisch
,
R.
,
Hauck
,
C. D.
, and
Osher
,
S.
,
2013
, “
Sparse Dynamics for Partial Differential Equations
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
17
), pp.
6634
6639
.
425.
Mackey
,
A.
,
Schaeffer
,
H.
, and
Osher
,
S.
, “
On the Compressive Spectral Method
,”
Multiscale Model. & Simul.
,
12
(
4
), pp.
1800
1827
.
426.
Tran
,
G.
,
Schaeffer
,
H.
,
Feldman
,
W. M.
, and
Osher
,
S. J.
,
2014
, “
An L1 Penalty Method for General Obstacle Problems
,” preprint
arXiv:1404.1370
.
427.
Shi
,
J. V.
,
Yin
,
W.
,
Sankaranarayanan
,
A. C.
, and
Baraniuk
,
R. G.
, “
Video Compressive Sensing for Dynamic MRI
,”
BMC Neurosci.
,
13
(
Suppl 1
), p.
183
.
428.
Jovanović
,
M. R.
,
Schmid
,
P. J.
, and
Nichols
,
J. W.
,
2014
, “
Sparsity-Promoting Dynamic Mode Decomposition
,”
Phys. Fluids
,
26
(
2
), p.
024103
.
429.
Brunton
,
S. L.
,
Proctor
,
J. L.
, and
Kutz
,
J. N.
, “
Compressive Sampling and Dynamic Mode Decomposition
,”
arXiv:1312.5186
.
430.
Gueniat
,
F.
,
Mathelin
,
L.
, and
Pastur
,
L.
,
2015
, “
A Dynamic Mode Decomposition Approach for Large and Arbitrarily Sampled Systems
,”
Phys. Fluids
,
27
(
2
), p.
025113
.
431.
Bright
,
I.
,
Lin
,
G.
, and
Kutz
,
J. N.
,
2013
, “
Compressive Sensing and Machine Learning Strategies for Characterizing the Flow Around a Cylinder With Limited Pressure Measurements
,”
Phys. Fluids
,
25
(
12
), p.
127102
.
432.
Brunton
,
S. L.
,
Tu
,
J. H.
,
Bright
,
I.
, and
Kutz
,
J. N.
,
2014
, “
Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems
,”
SIAM J. Appl. Dyn. Syst.
,
13
(
4
), pp.
1716
1732
.
433.
Tayler
,
A. B.
,
Holland
,
D. J.
,
Sederman
,
A. J.
, and
Gladden
,
L. F.
,
2012
, “
Exploring the Origins of Turbulence in Multiphase Flow Using Compressed Sensing MRI
,”
Phys. Rev. Lett.
,
108
(
26
), p.
264505
.
434.
Branicki
,
M.
, and
Majda
,
A. J.
,
2014
, “
Quantifying Bayesian Filter Performance for Turbulent Dynamical Systems Through Information Theory
,”
Commun. Math. Sci.
,
12
(
5
), pp.
901
978
.
435.
Bourguignon
,
J.-L.
,
Tropp
,
J.
,
Sharma
,
A.
, and
McKeon
,
B.
,
2014
, “
Compact Representation of Wall-Bounded Turbulence Using Compressive Sampling
,”
Phys. Fluids
,
26
(
1
), p.
015109
.
436.
Fu
,
X.
,
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2014
, “
Classification of Birefringence in Mode-Locked Fiber Lasers Using Machine Learning and Sparse Representation
,”
Opt. Express
,
22
(
7
), pp.
8585
8597
.
437.
Brunton
,
S. L.
,
Fu
,
X.
, and
Kutz
,
J. N.
,
2014
, “
Self-Tuning Fiber Lasers
,”
IEEE J. Sel. Top. Quantum Electron.
,
20
(
5
), p.
1101408
.
438.
Wright
,
J.
,
Yang
,
A.
,
Ganesh
,
A.
,
Sastry
,
S.
, and
Ma
,
Y.
,
2009
, “
Robust Face Recognition Via Sparse Representation
,”
IEEE Trans. Pattern Anal. Mach. Intell. (PAMI)
,
31
(
2
), pp.
210
227
.
439.
Kaiser
,
E.
,
Noack
,
B. R.
,
Cordier
,
L.
,
Spohn
,
A.
,
Segond
,
M.
,
Abel
,
M.
,
Daviller
,
G.
, and
Niven
,
R. K.
,
2014
, “
Cluster-Based Reduced-Order Modelling of a Mixing Layer
,”
J. Fluid Mech.
,
754
, pp.
365
414
.
440.
Burkardt
,
J.
,
Gunzburger
,
M.
, and
Lee
,
H.-C.
,
2004
, “
Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems
,”
SIAM J. Sci. Comput.
,
28
(
2
), pp.
459
484
.
441.
Schneider
,
T. M.
,
Eckhardt
,
B.
, and
Vollmer
,
J.
,
2007
, “
Statistical Analysis of Coherent Structures in Transitional Pipe Flow
,”
Phys. Rev. E
,
75
(
6
), pp.
66
313
.
442.
Gear
,
C. W.
,
Kevrekidis
,
I. G.
, and
Theodoropoulos
,
C.
, “
‘Coarse’ Integration/Bifurcation Analysis Via Microscopic Simulators: Micro-Galerkin Methods
,”
Comput. Chem. Eng.
,
26
(
7–8
), pp.
941
963
.
443.
Gorban
,
A.
,
Kazantzis
,
N. K.
,
Kevrekidis
,
I. G.
,
Öttinger
,
H.
, and
Theodoropoulos
,
C.
, eds.,
2006
,
Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
,
Springer-Verlag
,
Berlin
.
444.
Kevrekidis
,
I. G.
,
Gear
,
C. W.
,
Hyman
,
J. M.
,
Kevrekidis
,
P. G.
,
Runborg
,
O.
, and
Theodoropoulos
,
C.
,
2003
, “
Equation-Free, Coarse-Grained Multiscale Computation: Enabling Microscopic Simulators to Perform System-Level Analysis
,”
Commun. Math. Sci.
,
1
(
4
), pp.
715
762
.
445.
Sirisup
,
S.
,
Karniadakis
,
G. E.
,
Xiu
,
D.
, and
Kevrekidis
,
I. G.
,
2005
, “
Equation-Free/Galerkin-Free POD-Assisted Computation of Incompressible Flows
,”
J. Comput. Phys.
,
207
(
2
), pp.
568
587
.
446.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2002
, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(
2
), pp.
619
644
.
447.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2003
, “
Modeling Uncertainty in Flow Simulations Via Generalized Polynomial Chaos
,”
J. Comput. Phys.
,
187
(
1
), pp.
137
167
.
448.
Xiu
,
D.
,
2010
,
Numerical Methods for Stochastic Computations: A Spectral Method Approach
,
Princeton University Press
, Princeton, NJ.
449.
Grosek
,
J.
, and
Kutz
,
J. N.
,
2014
, “
Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video
,” preprint
arXiv:1404.7592
.
450.
Hemati
,
M. S.
,
Williams
,
M. O.
, and
Rowley
,
C. W.
,
2014
, “
Dynamic Mode Decomposition for Large and Streaming Datasets
,” preprint
arXiv:1406.7187
.
451.
Dawson
,
S.
,
Hemati
,
M.
,
Williams
,
M.
, and
Rowley
,
C.
,
2014
, “
Characterizing and Correcting for the Effect of Sensor Noise in the Dynamic Mode Decomposition
,”
Bull. Am. Phys. Soc.
,
59
(
20
), p.
428
.
452.
Aref
,
H.
,
1984
, “
Stirring by Chaotic Advection
,”
J. Fluid Mech.
,
143
, pp.
1
21
.
453.
Wiener
,
N.
,
1938
, “
The Homogeneous Chaos
,”
Am. J. Math.
,
60
(
4
), pp.
897
936
.
454.
Wan
,
X.
, and
Karniadakis
,
G. E.
,
2005
, “
An Adaptive Multi-Element Generalized Polynomial Chaos Method for Stochastic Differential Equations
,”
J. Comput. Phys.
,
209
(
2
), pp.
617
642
.
455.
Gerritsma
,
M.
,
van der Steen
,
J.-B.
,
Vos
,
P. E. J.
, and
Karniadakis
,
G. E.
,
2010
, “
Time-Dependent Generalized Polynomial Chaos
,”
J. Comput. Phys.
,
229
(
22
), pp.
8333
8363
.
456.
Luchtenburg
,
D. M.
,
Brunton
,
S. L.
, and
Rowley
,
C. W.
,
2014
, “
Long-Time Uncertainty Propagation Using Generalized Polynomial Chaos and Flow Map Composition
,”
J. Comput. Phys.
,
274
, pp.
783
802
.
457.
Le Maître
,
O. P.
, and
Knio
,
O. M.
,
2010
,
Spectral Methods for Uncertainty Quantification
,
Springer
, Dordrecht.
458.
Sapsis
,
T. P.
, and
Lermusiaux
,
P. F.
,
2009
, “
Dynamically Orthogonal Field Equations for Continuous Stochastic Dynamical Systems
,”
Physica D
,
238
(
23–24
), pp.
2347
2360
.
459.
Sapsis
,
T. P.
, and
Lermusiaux
,
P. F.
,
2012
, “
Dynamical Criteria for the Evolution of the Stochastic Dimensionality in Flows With Uncertainty
,”
Physica D
,
241
(
1
), pp.
60
76
.
460.
Haller
,
G.
,
2001
, “
Distinguished Material Surfaces and Coherent Structures in Three-Dimensional Fluid Flows
,”
Physica D
,
149
(
4
), pp.
248
277
.
461.
Haller
,
G.
,
2002
, “
Lagrangian Coherent Structures From Approximate Velocity Data
,”
Phys. Fluids
,
14
(
6
), pp.
1851
1861
.
462.
Shadden
,
S. C.
,
Lekien
,
F.
, and
Marsden
,
J. E.
,
2005
, “
Definition and Properties of Lagrangian Coherent Structures From Finite-Time Lyapunov Exponents in Two-Dimensional Aperiodic Flows
,”
Physica D
,
212
(
3–4
), pp.
271
304
.
463.
Green
,
M. A.
,
Rowley
,
C. W.
, and
Haller
,
G.
,
2007
, “
Detection of Lagrangian Coherent Structures in 3D Turbulence
,”
J. Fluid Mech.
,
572
, pp.
111
120
.
464.
Mathur
,
M.
,
Haller
,
G.
,
Peacock
,
T.
,
Ruppert-Felsot
,
J. E.
, and
Swinney
,
H. L.
,
2007
, “
Uncovering the Lagrangian Skeleton of Turbulence
,”
Phys. Rev. Lett.
,
98
(
14
), p.
144502
.
465.
Brunton
,
S. L.
, and
Rowley
,
C. W.
,
2010
, “
Fast Computation of FTLE Fields for Unsteady Flows: A Comparison of Methods
,”
Chaos
,
20
(
1
), p.
017503
.
466.
Farazmand
,
M.
, and
Haller
,
G.
,
2012
, “
Computing Lagrangian Coherent Structures From Their Variational Theory
,”
Chaos
,
22
(
1
), p.
013128
.
467.
Kafiabad
,
H. A.
,
Chan
,
P. W.
, and
Haller
,
G.
,
2012
, “
Lagrangian Detection of Aerial Turbulence for Landing Aircraft
,”
J. Appl. Meteorol. Climatol.
,
30
(
12
), pp.
2808
2819
.
468.
Shadden
,
S. C.
,
Astorino
,
M.
, and
Gerbeau
,
J. F.
,
2010
, “
Computational Analysis of an Aortic Valve Jet With Lagrangian Coherent Structures
,”
Chaos
,
20
(
1
), p.
017512
.
469.
Wilson
,
M. M.
,
Peng
,
J.
,
Dabiri
,
J. O.
, and
Eldredge
,
J. D.
,
2009
, “
Lagrangian Coherent Structures in Low Reynolds Number Swimming
,”
J. Phys.: Condens. Matter
,
21
(
20
), p.
204105
.
470.
Green
,
M. A.
,
Rowley
,
C. W.
, and
Smits
,
A. J.
,
2011
, “
The Unsteady Three-Dimensional Wake Produced by a Trapezoidal Pitching Panel
,”
J. Fluid Mech.
,
685
, pp.
117
145
.
471.
Peng
,
J.
, and
Dabiri
,
J. O.
,
2008
, “
The ‘Upstream Wake’ of Swimming and Flying Animals and Its Correlation With Propulsive Efficiency
,”
J. Exp. Biol.
,
211
(
16
), pp.
2669
2677
.
472.
Bollt
,
E. M.
,
Luttman
,
A.
,
Kramer
,
S.
, and
Basnayake
,
R.
,
2012
, “
Measurable Dynamics Analysis of Transport in the Gulf of Mexico During the Oil Spill
,”
Int. J. Bifurcation Chaos
,
22
(
3
), p.
1230012
.
473.
Lekien
,
F.
,
Coulliette
,
C.
,
Mariano
,
A. J.
,
Ryan
,
E. H.
,
Shay
,
L. K.
,
Haller
,
G.
, and
Marsden
,
J. E.
,
2005
, “
Pollution Release Tied to Invariant Manifolds: A Case Study for the Coast of Florida
,”
Physica D
,
210
(
1–2
), pp.
1
20
.
474.
Mezić
,
I.
,
Loire
,
S.
,
Fonoberov
,
V. A.
, and
Hogan
,
P.
,
2010
, “
A New Mixing Diagnostic and Gulf Oil Spill Movement
,”
Science
,
330
(
6003
), pp.
486
489
.
475.
Padberg
,
K.
,
Hauff
,
T.
,
Jenko
,
F.
, and
Junge
,
O.
,
2007
, “
Lagrangian Structures and Transport in Turbulent Magnetized Plasmas
,”
New J. Phys.
,
9
(
11
), p.
400
.
476.
Froyland
,
G.
, and
Padberg
,
K.
,
2009
, “
Almost-Invariant Sets and Invariant Manifolds—Connecting Probabilistic and Geometric Descriptions of Coherent Structures in Flows
,”
Physica D
,
238
(
16
), pp.
1507
1523
.
477.
Froyland
,
G.
,
Santitissadeekorn
,
N.
, and
Monahan
,
A.
,
2010
, “
Transport in Time-Dependent Dynamical Systems: Finite-Time Coherent Sets
,”
Chaos
,
20
(
4
), p.
043116
.
478.
Tallapragada
,
P.
, and
Ross
,
S. D.
,
2013
, “
A Set Oriented Definition of Finite-Time Lyapunov Exponents and Coherent Sets
,”
Commun. Nonlinear Sci. Numer. Simul.
,
18
(
5
), pp.
1106
1126
.
479.
Dellnitz
,
M.
,
Froyland
,
G.
, and
Junge
,
O.
,
2001
, “
The Algorithms Behind Gaio—Set Oriented Numerical Methods for Dynamical Systems
,”
Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
,
B.
Fieldler
, ed.,
Springer
, Dordrecht, pp.
145
174
.
480.
Dellnitz
,
M.
, and
Junge
,
O.
,
2002
, “
Set Oriented Numerical Methods for Dynamical Systems
,”
Handbook of Dynamical Systems
, Vol.
2
,
B.
Fiedler
, ed., Elsevier, Amsterdam, pp.
221
264
.
481.
Carlberg
,
K.
,
Bou-Mosleh
,
C.
, and
Farhat
,
C.
,
2011
, “
Efficient Non-Linear Model Reduction Via a Least-Squares Petrov–Galerkin Projection and Compressive Tensor Approximations
,”
Int. J. Numer. Methods Eng.
,
86
(
2
), pp.
155
181
.
482.
Avellaneda
,
M.
, and
Majda
,
A. J.
,
1990
, “
Mathematical Models With Exact Renormalization for Turbulent Transport
,”
Commun. Math. Phys.
,
131
(
2
), pp.
381
429
.
483.
Amsallem
,
D.
,
Zahr
,
M. J.
, and
Farhat
,
C.
,
2012
, “
Nonlinear Model Order Reduction Based on Local Reduced-Order Bases
,”
Int. J. Numer. Methods Eng.
,
92
(
10
), pp.
891
916
.
484.
Carlberg
,
K.
,
Farhat
,
C.
,
Cortial
,
J.
, and
Amsallem
,
D.
,
2013
, “
The GNAT Method for Nonlinear Model Reduction: Effective Implementation and Application to Computational Fluid Dynamics and Turbulent Flows
,”
J. Comput. Phys.
,
242
, pp.
623
647
.
485.
Everson
,
R.
, and
Sirovich
,
L.
,
1995
, “
Karhunen–Loeve Procedure for Gappy Data
,”
JOSA A
,
12
(
8
), pp.
1657
1664
.
486.
Willcox
,
K.
,
2006
, “
Unsteady Flow Sensing and Estimation Via the Gappy Proper Orthogonal Decomposition
,”
Comput. Fluids
,
35
(
2
), pp.
208
226
.
487.
Barrault
,
M.
,
Maday
,
Y.
,
Nguyen
,
N. C.
, and
Patera
,
A. T.
,
2004
, “
An ‘Empirical Interpolation’ Method: Application to Efficient Reduced-Basis Discretization of Partial Differential Equations
,”
C. R. Math.
,
339
(
9
), pp.
667
672
.
488.
Chaturantabut
,
S.
, and
Sorensen
,
D. C.
,
2010
, “
Nonlinear Model Reduction Via Discrete Empirical Interpolation
,”
SIAM J. Sci. Comput.
,
32
(
5
), pp.
2737
2764
.
489.
Chaturantabut
,
S.
, and
Sorensen
,
D. C.
,
2012
, “
A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
,”
SIAM J. Numer. Anal.
,
50
(
1
), pp.
46
63
.
490.
Peherstorfer
,
B.
,
Butnaru
,
D.
,
Willcox
,
K.
, and
Bungartz
,
H.-J.
,
2014
, “
Localized Discrete Empirical Interpolation Method
,”
SIAM J. Sci. Comput.
,
36
(
1
), pp.
A168
A192
.
491.
Majda
,
A. J.
, and
Kramer
,
P. R.
,
1999
, “
Simplified Models for Turbulent Diffusion: Theory, Numerical Modelling, and Physical Phenomena
,”
Phys. Rep.
,
314
(
4
), pp.
237
574
.
492.
Majda
,
A. J.
,
Harlim
,
J.
, and
Gershgorin
,
B.
,
2010
, “
Mathematical Strategies for Filtering Turbulent Dynamical Systems
,”
Discrete Contin. Dyn. Syst.
,
27
(
2
), pp.
441
486
.
493.
Majda
,
A. J.
, and
Harlim
,
J.
,
2012
,
Filtering Complex Turbulent Systems
,
Cambridge University Press
, Cambridge, UK.
494.
Maynard Gayme
,
D.
,
2010
, “
A Robust Control Approach to Understanding Nonlinear Mechanisms in Shear Flow Turbulence
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
495.
Marusic
,
I.
, and
Hutchins
,
N.
,
2005
, “
Experimental Study of Wall Turbulence: Implications for Control
,”
Transition and Turbulence Control
,
World Scientific
,
Singapore
, pp.
207
246
.
496.
Smits
,
A. J.
,
McKeon
,
B. J.
, and
Marusic
,
I.
,
2011
, “
High-Reynolds Number Wall Turbulence
,”
Annu. Rev. Fluid Mech.
,
43
(
1
), pp.
353
375
.
497.
Cacuci
,
D. G.
,
Navon
,
I. M.
, and
Ionescu-Bujor
,
M.
,
2013
,
Computational Methods for Data Evaluation and Assimilation
,
Chapman & Hall
,
Oxford, UK
.
498.
Cordier
,
L.
,
Abou El Majd
,
B.
, and
Favier
,
J.
,
2010
, “
Calibration of POD Reduced-Order Models Using Tikhonov Regularization
,”
Int. J. Numer. Methods Fluids
,
63
(
2
), pp.
269
296
.
499.
Kapur
,
J. N.
, and
Kevasan
,
H. K.
,
1992
,
Entropy Optimization Principles With Applications
, 1st ed.,
Academic Press
,
Boston
.
500.
Noack
,
B. R.
, and
Niven
,
R. K.
,
2012
, “
Maximum-Entropy Closure for a Galerkin System of Incompressible Shear Flow
,”
J. Fluid Mech.
,
700
, pp.
187
213
.
501.
Noack
,
B. R.
, and
Niven
,
R. K.
,
2013
, “
A Hierarchy of Maximum-Entropy Closures for Galerkin Systems of Incompressible Flows
,”
Comput. Math. Appl.
,
65
(
10
), pp.
1558
1574
.
502.
Andresen
,
B.
,
1983
, “
Finite-Time Thermodynamics
,”
Physics Laboratory II
, 1st ed.,
University of Copenhagen
,
Copenhagen, Denmark
.
503.
Noack
,
B. R.
,
Schlegel
,
M.
,
Ahlborn
,
B.
,
Mutschke
,
G.
,
Morzyński
,
M.
,
Comte
,
P.
, and
Tadmor
,
G.
,
2008
, “
A Finite-Time Thermodynamics of Unsteady Fluid Flows
,”
J. Non-Equilibr. Thermodyn.
,
33
(
2
), pp.
103
148
.
504.
Noack
,
B. R.
,
Schlegel
,
M.
,
Morzyński
,
M.
, and
Tadmor
,
G.
,
2010
, “
System Reduction Strategy for Galerkin Models of Fluid Flows
,”
Int. J. Numer. Methods Fluids
,
63
(
2
), pp.
231
248
.
505.
Taira
,
K.
,
2015
, private communication.
506.
Watts
,
D. J.
, and
Strogatz
,
S. H.
,
1998
, “
Collective Dynamics of ‘Small-World' Networks
,”
Nature
,
393
(
6684
), pp.
440
442
.
507.
Barabási
,
A.-L.
, and
Albert
,
R.
,
1999
, “
Emergence of Scaling in Random Networks
,”
Science
,
286
(
5439
), pp.
509
512
.
508.
Barabási
,
A.-L.
,
2009
, “
Scale-Free Networks: A Decade and Beyond
,”
Science
,
325
(
5939
), pp.
412
413
.
509.
Del Genio
,
C. I.
,
Gross
,
T.
, and
Bassler
,
K. E.
,
2011
, “
All Scale-Free Networks are Sparse
,”
Phys. Rev. Lett.
,
107
(
17
), p.
178701
.
510.
Barzel
,
B.
, and
Barabási
,
A.-L.
,
2013
, “
Universality in Network Dynamics
,”
Nat. Phys.
,
9
(
10
), pp.
673
681
.
511.
Newman
,
M. E.
,
2003
, “
The Structure and Function of Complex Networks
,”
SIAM Rev.
,
45
(
2
), pp.
167
256
.
512.
Leonard
,
N. E.
, and
Fiorelli
,
E.
,
2001
, “
Virtual Leaders, Artificial Potentials and Coordinated Control of Groups
,”
40th IEEE Conference on Decision and Control
, Orlando, FL, Dec. 4–7, Vol.
3
, pp.
2968
2973
.
513.
Olfati-Saber
,
R.
,
2006
, “
Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,”
IEEE Trans. Autom. Control
,
51
(
3
), pp.
401
420
.
514.
Balch
,
T.
, and
Arkin
,
R. C.
,
1998
, “
Behavior-Based Formation Control for Multirobot Teams
,”
IEEE Trans. Rob. Autom.
,
14
(
6
), pp.
926
939
.
515.
Cortes
,
J.
,
Martinez
,
S.
,
Karatas
,
T.
, and
Bullo
,
F.
,
2002
, “
Coverage Control for Mobile Sensing Networks
,”
IEEE International Conference on Robotics and Automation
(
ICRA '02
), Washington, DC, May 11–15, Vol.
2
, pp.
1327
1332
.
516.
Leonard
,
N. E.
,
Paley
,
D. A.
,
Lekien
,
F.
,
Sepulchre
,
R.
,
Fratantoni
,
D. M.
, and
Davis
,
R. E.
,
2007
, “
Collective Motion, Sensor Networks, and Ocean Sampling
,”
Proc. IEEE
,
95
(
1
), pp.
48
74
.
517.
Milo
,
R.
,
Shen-Orr
,
S.
,
Itzkovitz
,
S.
,
Kashtan
,
N.
,
Chklovskii
,
D.
, and
Alon
,
U.
,
2002
, “
Network Motifs: Simple Building Blocks of Complex Networks
,”
Science
,
298
(
5594
), pp.
824
827
.
518.
Luscombe
,
N. M.
,
Babu
,
M. M.
,
Yu
,
H.
,
Snyder
,
M.
,
Teichmann
,
S. A.
, and
Gerstein
,
M.
,
2004
, “
Genomic Analysis of Regulatory Network Dynamics Reveals Large Topological Changes
,”
Nature
,
431
(
7006
), pp.
308
312
.
519.
Low
,
S. H.
,
Paganini
,
F.
, and
Doyle
,
J. C.
,
2002
, “
Internet Congestion Control
,”
Control Syst.
,
22
(
1
), pp.
28
43
.
520.
Doyle
,
J. C.
,
Alderson
,
D. L.
,
Li
,
L.
,
Low
,
S.
,
Roughan
,
M.
,
Shalunov
,
S.
,
Tanaka
,
R.
, and
Willinger
,
W.
,
2005
, “
The “Robust Yet Fragile” Nature of the Internet
,”
Proc. Natl. Acad. Sci. U.S.A.
,
102
(
41
), pp.
14497
14502
.
521.
Rahmani
,
A.
,
Ji
,
M.
,
Mesbahi
,
M.
, and
Egerstedt
,
M.
,
2009
, “
Controllability of Multi-Agent Systems From a Graph-Theoretic Perspective
,”
SIAM J. Control Optim.
,
48
(
1
), pp.
162
186
.
522.
Liu
,
Y.-Y.
,
Slotine
,
J.-J.
, and
Barabasi
,
A.-L.
,
2011
, “
Controllability of Complex Networks
,”
Nature
,
473
(
7346
), pp.
167
173
.
523.
Lin
,
F.
,
Fardad
,
M.
, and
Jovanović
,
M. R.
,
2014
, “
Algorithms for Leader Selection in Stochastically Forced Consensus Networks
,”
IEEE Trans. Automat. Control
,
59
(
7
), pp.
1789
1802
.
524.
Cowan
,
N. J.
,
Chastain
,
E. J.
,
Vilhena
,
D. A.
,
Freudenberg
,
J. S.
, and
Bergstrom
,
C. T.
,
2012
, “
Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks
,”
PloS One
,
7
(
6
), p.
e38398
.
525.
Brockett
,
R.
,
2012
, “
Notes on the Control of the Liouville Equation
,”
Control of Partial Differential Equations
(Lecture Notes in Mathematics, Vol.
2048
),
F.
Alabau-Boussouira
,
R.
Brockett
,
O.
Glass
,
J.
Le Rousseau
, and
E.
Zuazua
, eds., Springer, Berlin, pp. 101–129.
526.
Hopf
,
E.
,
1951
, “
Statistical Hydromechanics and Functional Analysis
,”
J. Ration. Mech. Anal.
,
1
, pp.
87
123
.
527.
Bagheri
,
S.
,
2013
, “
Koopman-Mode Decomposition of the Cylinder Wake
,”
J. Fluid Mech.
,
726
, pp.
596
623
.
528.
Bagheri
,
S.
,
2014
, “
Effects of Weak Noise on Oscillating Flows: Linking Quality Factor, Floquet Modes and Koopman Spectrum
,”
Phys. Fluids
,
26
(
9
), p.
094104
.
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