Experimental and numerical study of the shear layer instability between two counter-rotating disks

Journal of Fluid Mechanics

Volumn 507, Issue , 2004, Pages 175-202

  Moisy, F ^a   Doare O ^a   Pasutto, T ^a   Daube, O ^b   Rabaud, M ^a  

^a Centre National de la Recherche Scientifique   (France)

^b UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; ROTATING DISKS; VELOCIMETERS; VELOCITY MEASUREMENT;

PARTICLE IMAGE VELOCIMETRY; SHEAR LAYER INSTABILITY;

SHEAR FLOW;

FLOW PATTERN; INSTABILITY; MATHEMATICAL ANALYSIS;

EID: 2642531243     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004008833     Document Type: Article

References (41)

1. AHLERS, G., CANNELL, D. S., DOMINGUEZ-LERMA, M. A. & HEINRICHS, R. 1986 Wavenumber selection and Eckhaus instability in Couette-Taylor flow. Physica D 23, 202-219.
2. BATCHELOR, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Q. J. Mech. Appl. Maths 4, 29-41.
3. BARBOSA, E. & DAUBE, O. 2001 A finite differences method in cylindrical coordinates for 3D incompressible flows. ECCOMAS CFD Conference, Swansea. UK (CD-ROM ISBN 0905 091 124).
4. BERGERON, K., COUTSIAS, E. A., LYNOV, J. P. & NIELSEN, A. H. 2000 Dynamical properties of forced shear layers in an annular geometry. J. Fluid Mech. 402, 255-289.
5. BLACKBURN, H. M. & LOPEZ, J. M. 2002 Modulated rotating waves in an enclosed swirling flow. J. Fluid Mech. 465, 33-58.
6. CHOMAZ, J. M., RABAUD, M., BASDEVANT, C. & COUDER, Y. 1988 Experimental and numerical investigation of a forced circular shear layer. J. Fluid Mech. 187, 115-140.
7. CROS, A. & LE GAL, P. 2002 Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14, 3755-3765.
8. DAUBE, O. & LE QUÉRÉ, P. 2002 Numerical investigation of the first bifurcation for the flow in a rotor-stator cavity of radial aspect ratio 10. Computers Fluids 31, 481-494.
9. DIJKSTRA, D. & VAN HEIJST, G. J. F. 1983 The flow between finite rotating disks enclosed by a cylinder. J. Fluid Mech. 128, 123-154.
10. DOLZHANSKII, F. V., KRYMOV, V. A. & MANIN, D. YU. 1990 Stability and vortex structures of quasi-two-dimensional shear flows. Sov. Phys. Usp 33 (7), 495-520.
11. DRAZIN, P. G. & REID, W. H. 1979 Hydrodynamic Instability. Cambridge University Press.
12. ESCUDIER, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating end wall. Exps. Fluids 2, 179-186.
13. FRÜH, W. G. & READ, P. L. 1999 Experiments on a barotropic rotating shear layer. Part 1. Instability and steady vortices. J. Fluid Mech. 383, 143-173.
14. GADOIN, E., LE QUÉRÉ, P. & DAUBE, O. 2001 A general methodology to investigate flow instabilities in complex geometries: application to natural convection in enclosures. Intl J. Numer. Meth. Fluids 37, 175-208.
15. GAUTHIER, G., GONDRET, P. & RABAUD, M. 1998 Motions of anisotropic particles: application to visualization of three-dimensional flows. Phys. Fluids 10, 2147-2154.
16. GAUTHIER, G., GONDRET, P. & RABAUD, M. 1999 Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder J. Fluid Mech. 386, 105-126.
17. GAUTHIER, G., GONDRET, P., MOISY, F. & RABAUD, M. 2002 Instabilities in the flow between co-and counter-rotating disks. J. Fluid Mech. 473, 1-21.
18. GELFGAT, A. Y., BAR-YOSEPH, P. Z. & SOLAN, A. 2001 Three-dimensional instability flow in a rotating lid-cylinder enclosure. J. Fluid Mech. 438, 363-377.
19. GODA, K. 1979 A multistep technique with implicit difference schemes for calculating two or three dimensional cavity flows. J. Comput. Phys. 30, 76-95.
20. HIDE, R. & TITMAN, C. W. 1967 Detached shear layers in a rotating fluid. J. Fluid Mech. 29, 39-60.
21. HUMPHREY, J. A. C., SCHULER, C. A. & WEBSTER, D. R. 1995 Unsteady laminar-flow between a pair of disks corotating in a fixed cylindrical enclosure. Phys. Fluids 7, 1225-1240.
22. HYMAN, J. M. & SHASHKOV, M. 1997 Natural discretization for the divergence, gradient and curl on logically rectangular grids. Comput. Math. Appl. 33, 81-104.
23. VON KÁRMÁN, T. 1921 Laminar und turbulente reibung. Z. Angew. Math. 1, 233-252.
24. VAN DE KONIJNENBERG, J. A., NIELSEN, A. H., RASMUSSEN, J. J. & STENUM, B. 1999 Shear flow instability in a rotating fluid. J. Fluid Mech. 387, 177-204.
25. LIOU, W. W. 1994 Linear instability of curved free shear layers. Phys. Fluids 6, 541-549.
26. LOPEZ, J. M. 1998 Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall. J. Fluid Mech. 359, 49-79.
27. LOPEZ, J. M., HART, J. E., MARQUES, F., KITTELMAN, S. & SHEN, J. 2002 Instability and mode interactions in a differentially-driven rotating cylinder. J. Fluid Mech. 462, 383-409.
28. MAMUM, C. K. & TUCKERMAN, L. S. 1995 Asymmetry and Hopf bifurcation in spherical Couette flow. Phys. Fluids 7, 80-91.
29. MARQUES, F., GELFGAT, A. YU. & LOPEZ, J. M. 2003 Tangent double Hopf bifurcation in a differentially rotating cylinder flow. Phys. Rev. E 68, 016310, 1-13.
30. MOISY, F., PASUTTO, T. & RABAUD, M. 2003 Instability patterns between counter-rotating disks. Nonlinear Processes Geophys. 10, 281-288.
31. NIINO, H. & MISAWA, N. 1984 An experimental and theoretical study of barotropic instability. J. Atmos. Sci. 41, 1992-2011.
32. NORE, C., TARTAR, M., DAUBE, O. & TUCKERMAN, L. S. 2004 Survey of instability thresholds of flow between exactly counter-rotating disks. J. Fluid Mech. (in press).
33. NORE, C., TUCKERMAN, L. S., DAUBE, O. & XIN, S. 2003 The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow. J. Fluid Mech. 477, 51-88.
34. RABAUD, M. & COUDER, Y. 1983 Instability of an annular shear layer. J. Fluid Mech. 136, 291-319.
35. SCHOUVEILER, L., LE GAL, P. & CHAUVE, M.-P. 2001 Instabilities of the flow between a rotating and stationary disk. J. Fluid Mech. 443, 329-350.
36. SERRE, E. & BONTOUX, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347-370.
37. SERRE, E., CRESPO DEL ARCO, E. & BONTOUX, P. 2001 Annular and spiral patterns in flows between rotating and stationary discs. J. Fluid Mech. 434, 65-100.
38. STEWARTSON, K. 1953 On the flow between two rotating coaxial disks. Proc. Camb. Phil. Soc. 49, 333-341.
39. TUCKERMAN, L. S. 1989 Steady-state solving via Stokes preconditioning: Recurrence relations for elliptic operators. 11th International Conference on Numerical Methods in Fluid Dynamics (ed. D. L. Dwoyer, M. Y. Hussaini & R. G. Voigt). Lecture Notes in Physics, vol. 323, pp. 573-577. Springer.
40. YANASE, S., FLORES, C., MÉTAIS, O. & RILEY, J. J. 1993 Rotating free-shear flows. I. Linear stability analysis Phys. Fluids A 5, 2725-2737.
41. ZANDBERGEN, P. J. & DIJKSTRA, D. 1987 Von Kármán swirling flows. Annu. Rev. Fluid Mech. 19, 465-91.