Planar straining and destraining of turbulence is an idealized form of turbulence-meanflow interaction that is representative of many complex engineering applications. This paper studies experimentally the response of turbulence subjected to a process involving planar straining, a brief relaxation and destraining. Subsequent analysis quantifies the impact of the applied distortions on model coefficients of various eddy viscosity subgrid-scale models. The data are obtained using planar particle image velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and destraining mean flows are produced by pushing and pulling a rectangular piston towards and away from the bottom wall of the tank. The velocity distributions are processed to yield the time evolution of mean subgrid dissipation rate, the Smagorinsky and dynamic model coefficients, as well as the mean subgrid-scale momentum flux during the entire process. It is found that the Smagorinsky coefficient is strongly scale dependent during periods of straining and destraining. The standard dynamic approach overpredicts the dissipation based Smagorinsky coefficient, with the model coefficient at scale Δ in the standard dynamic Smagorinsky model being close to the dissipation based Smagorinsky coefficient at scale 2Δ. The scale-dependent Smagorinsky model, which is designed to compensate for such discrepancies, yields unsatisfactory results due to subtle phase lags between the responses of the subgrid-scale stress and strain-rate tensors to the applied strains. Time lags are also observed for the SGS momentum flux at the larger filter scales considered. The dynamic and scale-dependent dynamic nonlinear mixed models do not show a significant improvement. These potential problems of SGS models suggest that more research is needed to further improve and validate SGS models in highly unsteady flows.

1.
Pope
,
S.
, 2000,
Turbulent Flows
,
Cambridge University Press
, Cambridge.
2.
Townsend
,
A.
, 1954, “
The Uniform Distortion of Homogeneous Turbulence
,”
Q. J. Mech. Appl. Math.
0033-5614,
7
(
1
), pp.
104
127
.
3.
Keffer
,
J.
, 1965, “
The Uniform Distortion of a Turbulent Wake
,”
J. Fluid Mech.
0022-1120,
22
, pp.
135
160
.
4.
Tucker
,
H.
, and
Reynolds
,
A.
, 1968, “
The Distortion of Turbulence by Irrotational Plane Strain
,”
J. Fluid Mech.
0022-1120,
32
, pp.
657
673
.
5.
Lee
,
M.
, and
Reynolds
,
W.
, 1985,
Numerical Experiments on the Structure of Homogenous Turbulence
, Stanford University Report, TF-24
6.
Liu
,
S.
,
Katz
,
J.
, and
Meneveau
,
C.
, 1999, “
Evolution and Modeling of Subgrid Scales During Rapid Straining of Turbulence
,”
J. Fluid Mech.
0022-1120,
387
, pp.
281
320
.
7.
Germano
,
M.
,
Piomeeli
,
U.
,
et al.
, 1991, “
A Dynamic Subgrid-Scale Eddy Viscosity Model
,”
Physica A
0378-4371,
3
, pp.
1760
1765
.
8.
Rogallo
,
R.
, and
Moin
,
P.
, 1984, “
Numerical Simulation of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
0066-4189,
16
, p.
99
.
9.
Reynolds
,
W.
, 1990, “
The Potential and Limitation of Direct and Large Eddy Simulations
,” in
Whither Turbulence? Or Turbulence at Crossroads
, edited by
J. L.
Lumley
,
Springer
, New York.
10.
Piomelli
,
U.
,
Cabot
,
W. H.
,
Moin
,
P.
, and
Lee
,
S.
, 1991, “
Subgrid-Scale Backscatter in Turbulent and Transitional Flows
,”
Phys. Fluids A
0899-8213,
3
(
7
), pp.
1766
1771
.
11.
Liu
,
S.
,
Meneveau
,
C.
, and
Katz
,
J.
, 1994, “
On the Properties of Similarity Subgrid-Scale Models as Deduced From Measurement in Turbulent Jet
,”
J. Fluid Mech.
0022-1120,
275
, pp.
83
119
.
12.
Lesieur
,
M.
, and
Metais
,
O.
, 1996, “
New Trends in Large-Eddy Simulations of Turbulence
,”
Annu. Rev. Fluid Mech.
0066-4189,
28
, pp.
45
82
.
13.
Smagorinsky
,
J.
, 1963, “
General Circulation Experiments With the Primitive Equations, Part 1: The Basic Experiment
,”
Mon. Weather Rev.
0027-0644,
91
, pp.
99
164
.
14.
Leonard
,
A.
, 1997, “
Large-Eddy Simulation of Chaotic Convection and Beyound
,”
AIAA Pap.
0146-3705 97-0204.
15.
Meneveau
,
C.
, and
Katz
,
J.
, 2000, “
Scale-Invariance and Turbulence Models for Large-Eddy Simulation
,”
Annu. Rev. Fluid Mech.
0066-4189,
32
, pp.
1
32
.
16.
Borue
,
V.
, and
Orszag
,
S. A.
, 1998, “
Local Energy Flux and Subgrid-Scale Statistics in Three Dimensional Turbulence
,”
J. Fluid Mech.
0022-1120,
366
, pp.
1
31
.
17.
Piomelli
,
U.
,
Moin
,
P.
, and
Ferziger
,
J.
, 1988, “
Model Consistency in Large Eddy Simulation of Turbulent Channel Flows
,”
Phys. Fluids
0031-9171,
31
(
7
), pp.
1884
1891
.
18.
Meneveau
,
C.
, 1994, “
Statistics of Turbulence Subgrid-Scale Stresses: Necessary Conditions and Experimental Tests
,”
Phys. Fluids
1070-6631,
6
(
2
), pp.
815
833
.
19.
O’Neil
,
J.
, and
Meneveau
,
C.
, 1997, “
Subgrid-Scale Stresses and Their Modelling in a Turbulent Plane Wake
,”
J. Fluid Mech.
0022-1120,
349
, pp.
253
293
.
20.
Tao
,
B.
,
Katz
,
J.
, and
Meneveau
,
C.
, 2002, “
Statistical Geometry of Subgrid-Scale Stresses Determined From Holographic Particle Image Velocimetry Measurements
,”
J. Fluid Mech.
0022-1120,
467
, pp.
35
78
.
21.
Porte-Agel
,
F.
,
Parlange
,
M. B.
,
Meneveau
,
C.
, and
Eichinger
,
W. E.
, 2001, “
A Priori Field Study of the Subgrid-Scale Heat Fluxes and Dissipation in the Atmospheric Surface Layer
,”
J. Atmos. Sci.
0022-4928,
58
, pp.
2673
2698
.
22.
Kleissl
,
J.
,
Meneveau
,
C.
, and
Parlange
,
M.
, 2003, “
On the Magnitude and Variability of Subgrid-Scale Eddy-Diffusion Coefficients in the Atmospheric Surface Layer
,”
J. Atmos. Sci.
0022-4928,
60
, pp.
2372
2388
.
23.
Lilly
,
D. K.
, 1967, “
The Representation of Small-Scale Turbulence in Numerical Simulation Experiments
,” in
Proc. IBM Scientific Computing Symp. Environ. Sci.
, p.
195
.
24.
Lilly
,
D. K.
, 1992, “
A Proposed Modification of the Germano Subgrid-Scale Closure Method
,”
Phys. Fluids A
0899-8213,
4
, pp.
633
635
.
25.
Meneveau
,
C.
, and
Lund
,
T. S.
, 1997, “
The Dynamic Model and Scale-Dependent Coefficient in the Viscous Range of Turbulence
,”
Phys. Fluids
1070-6631,
9
, pp.
3932
3934
.
26.
Porte-Agel
,
F.
,
Meneveau
,
C.
, and
Parlange
,
M.
, 2000, “
A Scale-Dependent Dynamic Model for Large-Eddy Simulation: Application to a Neutral Atmospheric Boundary Layer
,”
J. Fluid Mech.
0022-1120,
415
, pp.
261
284
.
27.
Bou-Zeid
,
E.
,
Meneveau
,
C.
, and
Parlange
,
M.
, 2005, “
A Scale-Dependent Lagrangian Dynamic Model for Large Eddy Simulation of Complex Turbulent Flow
,”
Phys. Fluids
1070-6631,
17
, p.
025105
.
28.
Meneveau
,
C.
,
Lund
,
T.
, and
Cabot
,
W.
, 1996, “
A Lagrangian Dynamic Subgrid-Scale Model of Turbulence
,”
J. Fluid Mech.
0022-1120,
319
, pp.
353
385
.
29.
Makita
,
H.
, 1991, “
Realization of a Large-Scale Turbulence Field in a Small Wind Tunnel
,”
Fluid Dyn. Res.
0169-5983,
8
, pp.
53
64
.
30.
Mydlarsky
,
L.
, and
Warhaft
,
Z.
, 1996, “
On the Onset of High-Reynolds-Number Grid-Generated Wind Tunnel Turbulence
,”
J. Fluid Mech.
0022-1120,
320
, pp.
331
368
.
31.
Roth
,
G.
,
Mascenik
,
D.
, and
Katz
,
J.
, 1999, “
Measurement of the Flow Structure and Turbulence Within a Ship Bow Wave
,”
Phys. Fluids
1070-6631,
11
, pp.
3512
3523
.
32.
Roth
,
G.
, and
Katz
,
J.
, 2001, “
Five Techniques for Increasing the Speed and Accuracy of PIV Interrogation
,”
Meas. Sci. Technol.
0957-0233,
12
, pp.
238
245
.
33.
Keane
,
R.
, and
Adrian
,
R.
, 1990, “
Optimization of Particle Image Velocimeters, Part I, Double Pulsed Systems
,”
Meas. Sci. Technol.
0957-0233,
1
, pp.
1202
1215
.
34.
Huang
,
H.
,
Dabiri
,
D.
, and
Gharib
,
M.
, 1997, “
On Errors of Digital Particle Image Velocimetry
,”
Meas. Sci. Technol.
0957-0233,
8
, pp.
1427
1440
.
35.
Chen
,
J.
,
Meneveau
,
C.
, and
Katz
,
J.
, 2005, “
Scale Interactions of Turbulence Subjected to a Straining-Relaxation-Destraining Cycle
,”
J. Fluid Mech.
0022-1120, submitted.
36.
Nimmo-Smith
,
W.
,
Katz
,
J.
, and
Osborn
,
T.
, 2005, “
Flow Structure in the Bottom Boundary Layer of the Coastal Ocean
,”
J. Phys. Oceanogr.
0022-3670,
35
(
1
), pp.
72
93
.
37.
Monin
,
A.
, and
Yaglom
,
A.
, 1971,
Statistical Fluid Mechanics
,
MIT Press
, Cambridge.
38.
Li
,
Y.
, and
Meneveau
,
C.
, 2004, “
Analysis of Mean Momentum Flux in Subgrid Models of Turbulence
,”
Phys. Fluids
1070-6631,
16
, pp.
3483
3486
.
39.
Wong
,
V. C.
, 1992, “
A Proposed Statistical-Dynamic Closure Method for the Linear or Nonlinear Subgrid-Scale Stresses
,”
Phys. Fluids
1070-6631, pp.
1080
1082
.
You do not currently have access to this content.