Advances in rapid distortion theory: From rotating shear flows to the baroclinic instability

Journal of Applied Mechanics, Transactions ASME

Volumn 73, Issue 3, 2006, Pages 449-460

  Salhi, Azlz ^a   Cambon, Claude ^b  

^a Campus Universitaire de Tunis   (Tunisia)

^b ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

HYDRODYNAMICS; MATHEMATICAL MODELS; REYNOLDS NUMBER; SHEAR FLOW; STABILITY; THERMAL STRATIFICATION; TURBULENT FLOW;

HYDRODYNAMIC STABILITY THEORY; PLANE QUADRATIC FLOWS; RAPID DISTORTION THEORY (RDT); STABILITY ANALYSIS;

ELECTRIC DISTORTION;

EID: 33745024834     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2150234     Document Type: Conference Paper

References (42)

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., 7, pp. 83-10
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 Anisotropie Turbulence," Annu. Rev. Fluid Mech., 31, pp. 1-5
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, 8, pp. 781-78
6. 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. 2300-230
7. Lifschitz, A., and Hameiri, E., 1991, "Local Stability Conditions in Fluid Dynamics," Phys. Fluids A, 3, pp. 2644-264
8. Nazarenko, S., Kevlahan, N. N., and Dubrulle, B., 1999, "A WKB Theory for Rapid Distortion of Inhomogeneous Turbulence," J. Fluid Mech., 390, pp. 325-34
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., 449, pp. 1-3
10. Benney, D. J., and Saffman, P. G., 1966, "Nonlinear Interactions of Random Waves in a Dispersive Medium," Proc. R. Soc. London, Ser. A, 289, pp. 301-32
11. Godeferd, F. S., Cambon, C., and Scott, J. F., 2001, "Report on the Workshop: Two-Point Closures and Their Application," J. Fluid Mech., 436, pp. 393-40
12. Staquet, C., and Sommeria, J., 2002, "Internal Gravity Waves: From Instabilities to Turbulence," Annu. Rev. Fluid Mech., 34, pp. 559-59
13. Cambon, C., Rubinstein, R., and Godeferd, F. S., 2004, "Advances in Wave Turbulence: Rapidly Rotating Flows," New J. Phys., 6(79), pp. 1-2
14. Cambon, C., Jacquin, L., and Lubrano, J-L., 1992, "Towards a New Reynolds Stress Model for Rotating Turbulent Flows," Phys. Fluids A, 4, pp. 812-82
15. Kassinos, S. C., Reynolds, W. C., and Rogers, M. M., 2000, "One-Point Turbulence Structure Tensors," J. Fluid Mech., 428, pp. 213-24
16. Craya, A., 1958, "Contribution á l'Analyse de la Turbulence Associée á des Vitesses Moyennes," P.S.T. No. 345 Ministére 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., 507, pp. 1-4
18. Salhi, A., 2002, "Similarities Between Rotation and Stratification Effects on Homogeneous Shear Flow," Theor. Comput. Fluid Dyn., 15, pp. 339-35
19. Bradshaw, P., 1969, "The Analogy Between Streamwise Curvature and Buoyancy in Turbulent Shear Flow," J. Fluid Mech., 36, pp. 177-18
20. Hunt, J. C. R., and Carruthers, D. J., 1990, "Rapid Distortion Theory and the 'Problems' of Turbulence," J. Fluid Mech., 212, pp. 497-53
21. Bayly, B. J., 1986, "Three-Dimensional Instability of Elliptical Flow," Phys. Rev. Lett., 57, pp. 2160-216
22. Rogallo, R. S., 1981, "Numerical Experiments in Homogeneous Turbulence," NASA TM 8131 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, 6, pp. 2084-210
24. Cambon, C., 2001, "Turbulence and Vortex Structures in Rotating and Stratified Flows," Eur. J. Mech. B/Fluids, 20, pp. 489-51
25. Salhi, A., and Cambon, C., 1997, "An Analysis of Rotating Shear Flow Using Linear Theory and DNS and LES Results," J. Fluid Mech., 347, pp. 171-19
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., 23, pp. 390-40
28. Lee, J. M., Kim, J., and Moin, P., 1990, "Structure of Turbulence at High Shear Rate," J. Fluid Mech., 216, pp. 561-58
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, 9(5), pp. 1307-131
31. Clark, T. T., and Zemach, C., 1995, "A Spectral Model Applied to Homogeneous Turbulence," Phys. Fluids, 7(7), pp. 1674-169
32. Touil, H., Bertoglio, J.-P., and Parpais, S., 2000, "A Spectral Closure Applied to Anisotropie Inhomogeneous Turbulence," In Advances in Turbulence VIII, C. Dopazo, ed. CIMNE, Barcelona, Spain, p. 68
33. Waleffe, F., 1990, "On the Three-Dimensional Instability of Strained Vortices," Phys. Fluids A, 2, pp. 76-8
34. Kerswell, R. R., 2002 "Elliptical Instability," Annu. Rev. Fluid Mech., 34, pp. 83-11
35. Godeferd, F. S., and Lollini, L., 1999, "DNS of Turbulence With Confinment and Rotation," J. Fluid Mech., 393, pp. 257-30
36. Smith, L. M., and Waleffe, F., 2002, "Generation of Slow, Larges Scales in Forced Rotating, Stratified Turbulence," J. Fluid Mech., 451, pp. 145-16
37. Cambon, C., Teissèdre, C., and Jeandel, D., 1985, "Etude d'Effets Couplès de Déformation et de Rotation sur une Turbulence Homogène," J. Mec. Theor. Appl., 4, pp. 629-65
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, 354, pp. 895-92
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. 79-11
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. 3, pp. 144-15
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., 104, pp. 247-26