On the three-dimensional instabilities of plane flows subjected to Coriolis force

Physics of Fluids

Volumn 9, Issue 5, 1997, Pages 1307-1316

  Leblanc, Stéphane ^a   Cambon, Claude ^a  

^a ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CORIOLIS EFFECT; SHEAR FLOW; VORTICES;

CORIOLIS FORCE; FLUID FLOW; INSTABILITY; PLANE FLOWS;

EID: 0030663699     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869273     Document Type: Article

References (45)

1. C. Cambon, J.-P. Benoít, L. Shao, and L. Jacquin, "Stability analysis and large-eddy simulation of rotating turbulence with organized eddies," J. Fluid Mech. 278, 175 (1994).
2. P. Bradshaw, "The analogy between streamline curvature and buoyancy in turbulent shear flow," J. Fluid Mech. 36, 177 (1969).
3. T. J. Pedley, "On the stability of viscous flow in a rapidly rotating pipe," J. Fluid Mech. 35, 97 (1969).
4. D. J. Tritton and P. A. Davies, "Instabilities in geophysical fluid dynamics," in Hydrodynamic Instabilities and the Transition to Turbulence, edited by H. L. Swinney and J. P. Gollub (SpringerVerlag, Berlin, 1981), p. 229.
5. D. J. Tritton, "Stabilization and destabilization of turbulent shear flow in a rotating fluid," J. Fluid Mech. 241, 503 (1992).
6. J. E. Hart, "Instability and secondary motion in a rotating channel flow," J. Fluid Mech. 45, 341 (1971).
7. D. K. Lezius and J. P. Johnston, "Roll-cell instabilities in rotating laminar and turbulent channel flows," J. Fluid Mech. 77, 153 (1976).
8. P. H. Alfredsson and H. Persson, "Instabilities in channel flow with system rotation," J. Fluid Mech. 202, 543 (1989).
9. A. A. Bidokhti and D. J. Tritton, "The structure of a turbulant free shear layer in a rotating fluid," J. Fluid Mech. 241, 469 (1992).
10. S. Yanase, C. Flores, O. Métais, and J. J. Riley, "Rotating free-shear flows. I. Linear stability analysis," Phys. Fluids A 5, 2725 (1993).
11. O. Métais, C. Flores, S. Yanase, J. J. Riley, and M. Lesieur, "Rotating free-shear flows. Part 2. Numerical simulations," J. Fluid Mech. 293, 47 (1995).
12. N. Tillmark and P. H. Alfredsson, "Experiments on rotating plane Couette flow," in Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, The Netherlands, 1996), p. 391.
13. L. Tarbouriech and D. Renouard, "Stabilisation et déstabilisation par la rotation d'un sillage plan turbulent," C. R. Acad. Sci. Paris t 323, II b, 391 (1996).
14. R. C. Kloosterziel, "Barotropic vortices in a rotating fluid," Ph.D. thesis, Univ. Utrecht, The Netherlands (1990).
15. R. C. Kloosterziel and G. J. F. van Heijst, "An experimental study of unstable barotropic vortices in a rotating fluid," J. Fluid Mech. 223, 1 (1991).
16. E. J. Hopfinger, F. K. Browand, and Y. Gagne, "Turbulence and waves in a rotating tank," J. Fluid Mech. 125, 505 (1982).
17. P. Bartello, O. Métais, and M. Lesieur, "Coherent structures in rotating three-dimensional turbulence," J. Fluid Mech. 273, 1 (1994).
18. E. J. Hopfinger and G. J. F. van Heijst, "Vortices in rotating fluids," Annu. Rev. Fluid Mech. 25, 241 (1993).
19. G. F. Carnevale, M. Briscolini, R. C. Kloosterziel, and G. K. Vallis, "Three-dimensionally perturbed vortex tubes in a rotating flow," to appear in J. Fluid Mech.
20. I. Mutabazi, C. Normand, and J. E. Wesfreid, "Gap size effects on centrifugally and rotationally driven instabilities," Phys. Fluids A 4, 1199 (1992).
21. A. Aouidef, J. E. Wesfreid, and I. Mutabazi, "Coriolis effects on Görtler vortices in a boundary-layer flow on a concave wall," AIAA J. 30, 2779 (1992).
22. I. Mutabazi and J. E. Wesfreid, "Coriolis force and centrifugal force induced flow instabilities," in Instabilities and Nonequilibrium Structures IV, edited by E. Tirapegui and W. Zeller (Kluwer, The Netherlands, 1993), p. 301.
23. A. Zebib and A. Bottaro, "Goertler vortices with system rotation: Linear theory," Phys. Fluids A 5, 1206 (1993).
24. O. J. E. Matsson, "Time-dependent instabilities in curved rotating channel flow," Phys. Fluids A 5, 1514 (1993).
25. R. R. Lagnado, N. Phan-Thien, and L. G. Leal, "The stability of two-dimensional linear flows," Phys. Fluids 27, 1094 (1984).
26. R. T. Pierrehumbert, "Universal short-wave instability of two-dimensional eddies in an inviscid fluid," Phys. Rev Lett. 57, 2157 (1986).
27. B. J. Bayly, "Three-dimensional instability of elliptical flow," Phys. Rev. Lett. 57, 2160 (1986).
28. A. D. D. Craik and W. O. Criminale, "Evolution of wavelike disturbances in shear flows: A class of exact solutions of the Navier-Stokes equations," Proc. R. Soc. London. Ser. A 406, 13 (1986).
29. A. D. D. Craik, "The stability of unbounded two- and three-dimensional flows subject to body forces: Some exact solutions," J. Fluid Mech. 198, 275 (1989).
30. F. Waleffe, "On the three-dimensional instability of strained vortices," Phys. Fluids A 2, 76 (1990).
31. G. K. Batchelor and I. Proudman, "The effect of rapid distortion on a fluid in turbulent motion," Q. J. Mech. Appl. Math. 7, 83 (1954).
32. C. Cambon, "Etude spectrale d'un champ turbulent incompressible soumis à des effets couplés de déformation et de rotation imposés extérieurement," Ph.D. thesis, Univ. Lyon I, France (1982).
33. C. Cambon, C. Teissèdre, and D. Jeandel, "Etude d'effets couplés de déformation et de rotation sur une turbulence homogène," J. Méc. Théo Appl. 4, 629 (1985).
34. C. G. Speziale, T. B. Gatski, and N. Mac Giolla Mhuiris, "A critical comparison of turbulence models for homogeneous shear flows in a rotating frame," Phys. Fluids A 2, 1678 (1990).
35. A. Sahli and C. Cambon, "Analysis of rotating shear flow using linear approach and DNS-LES results," J. Fluid Mech. (submitted).
36. B. J. Bayly, "Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows," Phys. Fluids 31, 56 (1988). Referred to as B88.
37. J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, New York, 1979).
38. S. Leblanc and C. Cambon, "Stability of the Stuart vortices in a rotating frame," in Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, The Netherlands, 1996), p. 351.
39. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
40. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
41. B. J. Bayly, S. A. Orszag, and T. Herbert, "Instability mechanisms in shear-flow transition," Annu. Rev. Fluid Mech. 20, 359 (1988).
42. S. Friedlander and M. M. Vishik, "Instability criteria for the flow of an inviscid incompressible fluid," Phys. Rev. Lett. 66, 2204 (1991).
43. A. Lifschitz and E. Hameiri, "Local stability conditions in fluid dynamicics," Phys. Fluids A 3, 2644 (1991).
44. S. Tanveer and C. G. Speziale, "Singularities of the Euler equation and hydrodynamic stability," Phys. Fluids A 5, 1456 (1993).
45. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).