Spin-up of stratified rotating flows at large Schmidt number: Experiment and theory

Journal of Fluid Mechanics

Volumn 389, Issue , 1999, Pages 169-207

  Hewitt, R E ^a,b   Davies, P A ^b   Duck, P W ^a   Foster, M R ^c  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF DUNDEE   (United Kingdom)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYER FLOW; CONES; EIGENVALUES AND EIGENFUNCTIONS; SPECTRUM ANALYSIS; STEADY FLOW;

SCHMIDT NUMBER;

ROTATIONAL FLOW;

EID: 0032624438     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099004905     Document Type: Article

References (40)

1. BALAKUMAR, P. & MALIK, M. R. 1992 Discrete modes and continuous spectra in supersonic boundary layers. J. Fluid Mech. 239, 631.
2. BENTON, E. R. & CLARK, A. 1974 Spin-up. Ann. Rev. Fluid Mech. 6, 257.
3. BODONYI, R. J. 1978 On the unsteady similarity equations for the flow above a rotating disc in a rotating fluid. Q. Appl. Math. Mech. 31, 461.
4. BODONYI, R. J. & NG, B. S. 1984 On the stability of the similarity solutions for swirling flow above an infinite rotating disk. J. Fluid Mech. 144, 311.
5. BODONYI, R. J. & STEWARTSON, K. 1977 The unsteady laminar boundary layer on a rotating disk in a counter-rotating fluid. J. Fluid Mech. 79, 669.
6. BOUBNOV, B. M., GLEDZER, E. B. & HOPFINGER E. J. 1995 Stratified circular Couette-flow - instability and flow regimes. J. Fluid Mech. 292, 333.
7. BUZYNA, G. & VERONIS, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579.
8. DALZIEL, S. B. 1992 Decay of rotating turbulence - some particle tracking experiments. Appl. Sci. Res. 49, 217.
9. DAVIES, P. A., FERNANDO, H. J. S., BESLEY, P. & SIMPSON, R. J. 1991 The generation and spreading of a turbulent mixed layer in a rotating stratified fluid. J. Geophys. Res. 96, NC7, 12567.
10. DUCK, P. W., FOSTER, M. R. & HEWITT, R. E. 1997 On the boundary layer arising in the spin-up of a stratified fluid in a container with sloping walls. J. Fluid. Mech. 335, 233 (referred to herein as DFH).
11. GARRETT, C., MACCREADY, P. & RHINES P. 1993 Boundary mixing and arrested Ekman layers: Rotating stratified flow near a sloping boundary. Ann. Rev. Fluid Mech. 25, 291.
12. GREENSPAN, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
13. GREENSPAN, H. P. & HOWARD, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid. Mech. 17, 385.
14. GREENSPAN, H. P. & WEINBAUM, S. 1965 On nonlinear spin-up of a rotating fluid. J. Maths and Phys. 44, 66.
15. GREGORY, N., STUART, J. T. & WALKER, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155.
16. GROSCH, C. E. & SALWEN, H. 1978 The continuous spectrum of the Orr-Sommerfeld equation. Part 1. The spectrum and eigenfunctions. J. Fluid Mech. 87, 33.
17. HOLTON, J. R. 1965 The influence of viscous boundary layers on transient motions in a stratified rotating fluid, Part I. J. Atmos. Sci. 22, 402.
18. LINGWOOD, R. J. 1996 An experimental study of absolute instability of the rotating-disk boundary layer flow. J. Fluid Mech. 314, 373.
19. LINGWOOD, R. J. 1997 Absolute instability of the Ekman layer and related flows. J. Fluid Mech. 331, 405.
20. LOOPEZ, J. M. & WEIDMAN, P. D. 1996 Stability of stationary end wall boundary layers during spin-down. J. Fluid Mech. 326, 373.
21. MACCREADY, P. & RHINES, P. B. 1991 Buoyant inhibition of Ekman transport on a slope and its effect on stratified spin up. J. Fluid. Mech. 223, 631.
22. MACK, L. M. 1976 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497.
23. MURDOCK, J. W. & STEWARTSON, K. 1977 Spectra of the Orr-Sommerfeld equation. Phys. Fluids 20, 1404.
24. NEITZEL, G. P. & DAVIS, S. H. 1980 Energy stability theory of decelerating swirl flows. Phys. Fluids 23, 432.
25. NEITZEL, G. P. & DAVIS, S. H. 1981 Centrifugal instabilities during spin-down to rest in finite cylinders. J. Fluid Mech. 102, 329.
26. OSTER, G. 1965 Density gradients. Sci. Am. 213, 70.
27. PEDLOSKY, J. 1967 The spin-up of a stratified fluid. J. Fluid. Mech. 28, 463.
28. ROGERS, M. H. & LANCE. G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of a rotating disk. J. Fluid Mech. 7, 617.
29. SAKURAI, T. 1969 Spin down problem of a rotating stratified fluid in thermally insulated circular cylinders. J. Fluid Mech. 37, 689.
30. SALWEN, H. & GROSCH, C. E. 1981 The continuous spectrum of the Orr-Sommerfeld equation. Part 2. eigenfunction expansions. J. Fluid Mech. 104, 445.
31. SPENCE, G. S. M., FOSTER, M. R. & DAVIES, P. A. 1992 The transient response of a contained rotating stratified fluid to impulsively started surface forcing. J. Fluid Mech. 243, 33.
32. TATRO, P. R. & MOLLÖ-CHRISTENSEN, E. L. 1967 Experiments on Ekman layer instability. J. Fluid Mech. 28, 531.
33. THORPE, S. A. 1987 Current and temperature variability on the continental slope. Phil. Trans. R. Soc. Lond. A 323, 471.
34. VALENTINE, D. T. & MILLER, K. D. 1994 Generation of ring vortices in axisymmetric spin-down: A numerical investigation Phys. Fluids 6, 1535.
35. VERONIS, G. 1970 The analogy between rotating and stratified fluids. Ann. Rev. Fluid. Mech. 2, 37.
36. WALIN, G. 1969 Some aspects of time-dependent motion of a stratified fluid. J. Fluid Mech. 36, 289.
37. WEDEMEYER, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid. Mech. 20, 383.
38. WILKINSON, S. P. & MALIK, M. R. 1985 Stability experiments in the flow over a rotating disk. AIAA J. 23, 588.
39. WIMMER, M. 1995 An experimental investigation of Taylor vortex flow between conical cylinders. J. Fluid Mech. 292, 205.
40. ZANDBERGEN, P. J. & DIJKSTRA, D. 1987 Von Karman swirling flows. Ann. Rev. Fluid Mech. 19, 465.