The essentials of rapid distortion theory (RDT) are briefly recalled for homogeneous turbulence subjected to rotational mean flows, including its linkage to stability analysis. The latter “linkage” is of particular importance from our viewpoint, since it also attracted the attention of Charles Speziale, resulting in at least two papers [Speziale, C. G., Abid, R., and Blaisdell, G. A., 1996, “On the Consistency of Reynolds Stress Turbulence Closures With Hydrodynamic Stability Theory,” Phys. Fluids, 8, pp. 781–788 and Salhi, A., Cambon, C., and Speziale, C. G., 1997, “Linear Stability Analysis of Plane Quadratic Flows in a Rotating Frame,” Phys. Fluids, 9(8), pp. 2300–2309] with particular emphasis on rotating flows. New analytical solutions and related RDT results are presented for shear flows including buoyancy forces, with system rotation or mean density stratification. Finally, combining shear, rotation and stratification, RDT is shown to be pertinent to revisiting the baroclinic instability. This instability results from the tilting of mean isopycnal surfaces under combined effects of vertical shear and system rotation, in a vertically (stably) stratified medium rotating around the vertical direction. In addition, the challenge of reproducing RDT dynamics in single-point closure models is briefly discussed, from the viewpoint of structure-based modeling [Cambon C., Jacquin, L., and Lubrano, J.-L., 1992, “Towards a New Reynolds Stress Model for Rotating Turbulent Flows,” Phys. Fluids A, 4, pp. 812–824 and Kassinos, S. C., Reynolds, W. C., and Rogers, M. M., 2000, “One-Point Turbulence Structure Tensors,” J. Fluid Mech., 428, pp. 213–248.

1.
Townsend
,
A. A.
, 1956,
The Structure of Turbulent Shear Flow
Revised version.
Cambridge University Press
,
Cambridge, UK
.
2.
Batchelor
,
G. K.
, and
Proudman
,
I.
, 1954, “
The Effect of Rapid Distortion in a Fluid in Turbulent Motion
,”
Q. J. Mech. Appl. Math.
0033-5614,
7
, pp.
83
103
.
3.
Moffat
,
H. K.
, 1967, “
The Interaction of Turbulence With a Strong Shear
,”
A. M.
Yaglom
and
V. I.
Tatarsky
, eds.,
Atmospheric Turbulence and Radio Wave Propagation
NAUCA
,
Moscow
.
4.
Cambon
,
C.
, and
Scott
,
J. F.
, 1999, “
Linear and Nonlinear Models of Anisotropic Turbulence
,”
Annu. Rev. Fluid Mech.
0066-4189,
31
, pp.
1
53
.
5.
Speziale
,
C. G.
,
Abid
,
R.
, and
Blaisdell
,
G. A.
, 1996, “
On the Consistency of Reynolds Stress Turbulence Closures With Hydrodynamic Stability Theory
,”
Phys. Fluids
1070-6631,
8
, pp.
781
788
.
6.
Salhi
,
A.
,
Cambon
,
C.
, and
Speziale
,
C. G.
, 1997, “
Linear Stability Analysis of Plane Quadratic Flows in a Rotating Frame
,”
Phys. Fluids
1070-6631,
9
(
8
), pp.
2300
2309
.
7.
Lifschitz
,
A.
, and
Hameiri
,
E.
, 1991, “
Local Stability Conditions in Fluid Dynamics
,”
Phys. Fluids A
0899-8213,
3
, pp.
2644
2641
.
8.
Nazarenko
,
S.
,
Kevlahan
,
N. N.
, and
Dubrulle
,
B.
, 1999, “
A WKB Theory for Rapid Distortion of Inhomogeneous Turbulence
,”
J. Fluid Mech.
0022-1120,
390
, pp.
325
348
.
9.
Godeferd
,
F. S.
,
Cambon
,
C.
, and
Leblanc
,
S.
, 2001, “
Zonal Approach to Centrifugal, Elliptic and Hyperbolic Instabilities in Suart Vortices With External Rotation
,”
J. Fluid Mech.
0022-1120,
449
, pp.
1
37
.
10.
Benney
,
D. J.
, and
Saffman
,
P. G.
, 1966, “
Nonlinear Interactions of Random Waves in a Dispersive Medium
,”
Proc. R. Soc. London, Ser. A
1364-5021,
289
, pp.
301
320
.
11.
Godeferd
,
F. S.
,
Cambon
,
C.
, and
Scott
,
J. F.
, 2001, “
Report on the Workshop: Two-Point Closures and Their Application
,”
J. Fluid Mech.
0022-1120,
436
, pp.
393
407
.
12.
Staquet
,
C.
, and
Sommeria
,
J.
, 2002, “
Internal Gravity Waves: From Instabilities to Turbulence
,”
Annu. Rev. Fluid Mech.
0066-4189,
34
, pp.
559
593
.
13.
Cambon
,
C.
,
Rubinstein
,
R.
, and
Godeferd
,
F. S.
, 2004, “
Advances in Wave Turbulence: Rapidly Rotating Flows
,”
New J. Phys.
1367-2630,
6
(
79
), pp.
1
29
.
14.
Cambon
,
C.
,
Jacquin
,
L.
, and
Lubrano
,
J-L.
, 1992, “
Towards a New Reynolds Stress Model for Rotating Turbulent Flows
,”
Phys. Fluids A
0899-8213,
4
, pp.
812
824
.
15.
Kassinos
,
S. C.
,
Reynolds
,
W. C.
, and
Rogers
,
M. M.
, 2000, “
One-Point Turbulence Structure Tensors
,”
J. Fluid Mech.
0022-1120,
428
, pp.
213
248
.
16.
Craya
,
A.
, 1958, “
Contribution à l’Analyse de la Turbulence Associée à des Vitesses Moyennes
,” P.S.T. No. 345 Ministère de l’air, France.
17.
Hanazaki
,
H.
, and
Hunt
,
J. C. R.
, 2004, “
Linear Processes in Unsteady Stably Stratified Sheared Turbulence With Mean Shear
,”
J. Fluid Mech.
0022-1120,
507
, pp.
1
42
.
18.
Salhi
,
A.
, 2002, “
Similarities Between Rotation and Stratification Effects on Homogeneous Shear Flow
,”
Theor. Comput. Fluid Dyn.
0935-4964,
15
, pp.
339
358
.
19.
Bradshaw
,
P.
, 1969, “
The Analogy Between Streamwise Curvature and Buoyancy in Turbulent Shear Flow
,”
J. Fluid Mech.
0022-1120,
36
, pp.
177
181
.
20.
Hunt
,
J. C. R.
, and
Carruthers
,
D. J.
, 1990, “
Rapid Distortion Theory and the ‘Problems’ of Turbulence
,”
J. Fluid Mech.
0022-1120,
212
, pp.
497
532
.
21.
Bayly
,
B. J.
, 1986, “
Three-Dimensional Instability of Elliptical Flow
,”
Phys. Rev. Lett.
0031-9007,
57
, pp.
2160
2163
.
22.
Rogallo
,
R. S.
, 1981, “
Numerical Experiments in Homogeneous Turbulence
,” NASA TM 81315. Available from NASA Scientific & Technical Information (help@sti.nasa.gov).
23.
Godeferd
,
F. S.
, and
Cambon
,
C.
, 1994, “
Detailed Investigation of Energy Transfers in Homogeneous Stratified Turbulence
,”
Phys. Fluids
1070-6631,
6
, pp.
2084
2100
.
24.
Cambon
,
C.
, 2001, “
Turbulence and Vortex Structures in Rotating and Stratified Flows
,”
Eur. J. Mech. B/Fluids
0997-7546,
20
, pp.
489
510
.
25.
Salhi
,
A.
, and
Cambon
,
C.
, 1997, “
An Analysis of Rotating Shear Flow Using Linear Theory and DNS and LES Results
,”
J. Fluid Mech.
0022-1120,
347
, pp.
171
195
.
26.
Drazin
,
P. G.
, and
Reid
,
W. H.
, 1981,
Hydrodynamic Stability
,
Cambridge University Press
,
Cambridge, UK
.
27.
Stone
,
P. H.
, 1966, “
On Non-Geostrophic Baroclinic Instability
,”
J. Atmos. Sci.
0022-4928,
23
, pp.
390
400
.
28.
Lee
,
J. M.
,
Kim
,
J.
, and
Moin
,
P.
, 1990, “
Structure of Turbulence at High Shear Rate
,”
J. Fluid Mech.
0022-1120,
216
, pp.
561
583
.
29.
Greenspan
,
H. P.
, 1968,
The Theory of Rotating Fluids
,
Cambridge University Press
,
Cambridge, UK
.
30.
Leblanc
,
S.
, and
Cambon
,
C.
, 1997, “
On the Three-Dimensional Instabilities of Plane Flows Subjected to Coriolis Force
,”
Phys. Fluids
1070-6631,
9
(
5
), pp.
1307
1316
.
31.
Clark
,
T. T.
, and
Zemach
,
C.
, 1995, “
A Spectral Model Applied to Homogeneous Turbulence
,”
Phys. Fluids
1070-6631,
7
(
7
), pp.
1674
1694
.
32.
Touil
,
H.
,
Bertoglio
,
J.-P.
, and
Parpais
,
S.
, 2000, “
A Spectral Closure Applied to Anisotropic Inhomogeneous Turbulence
,” In
Advances in Turbulence VIII
,
C.
Dopazo
, ed.
CIMNE
,
Barcelona, Spain
, p.
689
.
33.
Waleffe
,
F.
, 1990, “
On the Three-Dimensional Instability of Strained Vortices
,”
Phys. Fluids A
0899-8213,
2
, pp.
76
80
.
34.
Kerswell
,
R. R.
, 2002, “
Elliptical Instability
,”
Annu. Rev. Fluid Mech.
0066-4189,
34
, pp.
83
113
.
35.
Godeferd
,
F. S.
, and
Lollini
,
L.
, 1999, “
DNS of Turbulence With Confinment and Rotation
,”
J. Fluid Mech.
0022-1120,
393
, pp.
257
308
.
36.
Smith
,
L. M.
, and
Waleffe
,
F.
, 2002, “
Generation of Slow, Larges Scales in Forced Rotating, Stratified Turbulence
,”
J. Fluid Mech.
0022-1120,
451
, pp.
145
168
.
37.
Cambon
,
C.
,
Teissèdre
,
C.
, and
Jeandel
,
D.
, 1985, “
Etude d’Effets Couplés de Déformation et de Rotation sur une Turbulence Homogène
,”
J. Mec. Theor. Appl.
0750-7240,
4
, pp.
629
657
.
38.
Bayly
,
B. J.
,
Holm
,
D. D.
, and
Lifschitz
,
A.
, 1996, “
Three-Dimensional Stability of Elliptical Vortex Columns in External Strain Flows
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
354
, pp.
895
926
.
39.
Riley
,
J. J.
,
Metcalfe
,
R. W.
, and
Weisman
,
M. A.
, 1981, “
DNS of Homogeneous Turbulence in Density Stratified Fluids
,” In
Proc. AIP Conf. on Nonlinear Properties of Internal Waves
,
B. J.
West
, ed.,
AIP
,
New York
, pp.
79
112
.
40.
Rogers
,
M. M.
, 1991, “
The Structure of a Passive Scalar Field With a Uniform Gradient in Rapidly Sheared Homogeneous Turbulent Flow
,”
Phys. Fluids A
0899-8213,
3
, pp.
144
154
.
41.
Fermetures Compatibles Avec la Théorie de Distorsion Rapide en Turbulence Homogène
,” C. R. Acad. Sciences Paris. (in press).
42.
Cambon
,
C.
,
Jeandel
,
D.
, and
Mathieu
,
J.
, 1981, “
Spectral Modelling of Homogeneous Non-Isotropic Turbulence
,”
J. Fluid Mech.
0022-1120,
104
, pp.
247
262
.
This content is only available via PDF.
You do not currently have access to this content.