The instability and breaking of long internal waves

Journal of Fluid Mechanics

Volumn 543, Issue , 2005, Pages 107-136

  Troy, Cary D ^a   Koseff, Jeffrey R ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF FLUIDS; FLOW VISUALIZATION; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; SHEAR WAVES;

INTERNAL WAVE BREAKING; KELVIN-HELMHOLTZ SHEAR INSTABILITY; RICHARDSON NUMBERS;

GRAVITY WAVES;

FLOW VISUALIZATION; INTERNAL WAVE; WAVE BREAKING;

EID: 28244474164     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005006798     Document Type: Article

References (69)

1. Alayhari, A. & Longmire, E. K. 1994 Particle image velocimetry in a variable density flow: Application to a dynamically evolving microburst. Exps. Fluids 17, 434-440.
2. Antenucci, J. P. & Imberger, J. 2001 On internal waves near the high frequency limit in an enclosed basin. J. Geophys. Res. 106, 22465-22472.
3. Atsavapranee, P. & Gharib, M. 1997 Structures in stratified plane mixing layers and the effects of cross-shear. J. Fluid Mech. 342, 53-86.
4. Boegman, L., Imberger, J., Ivey, G. N. & Antenucci, J. P. 2003 High-frequency internal waves in large stratified lakes. Limnol. Oceanogr. 48, 895-919.
5. Caulfield, C. P. & Peltier, W. R. 2000 The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech. 413, 1-47.
6. Daviero, G. J., Roberts, P. J. W. & Maile, K. 2001 Refractive index matching in large-scale stratified experiments. Exps. Fluids 31, 119-126.
7. Davis, R. E. & Acrivos, A. 1967 The stability of oscillatory internal waves. J. Fluid Mech. 30, 723-736.
8. Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of inviscid fluid. Adv. Appl. Mech. 9, 1-89.
9. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
10. Fringer, O. B. & Street, R. L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494, 319-353.
11. Fritts, D. C. 1989 A review of gravity wave saturation processes, effects, and variability in the middle atmosphere. PAGEOPH 130 (2), 343-371.
12. Fritts, D. C., Isler, J. R., Hecht, J. H., Walterscheid, R. L. & Andreassen, Ø. 1997 Wave breaking signatures in OH airglow and sodium densities and temperatures, 2, simulation of wave and instability structures. J. Geophys. Res. 102, D6, 6669-6684.
13. Gill, A. E. 1982 Atmosphere-Ocean Dynamics. Academic.
14. Gregg, M. C. 1987 Diapycnal mixing in the thermocline: A review. J. Geophys. Res. 92, 5249-5286.
15. Gregg, M. C., Winkel, D. P. & Sanford, T. B. 1993 Varieties of fully resolved spectra of vertical shear. J. Phys. Oceanogr. 23, 124-141.
16. Grue, J., A. Jensen, A., Rusas, P. & Sveen, J. K. 2000 Breaking and broadening of internal solitary wavess. J. Fluid Mech. 413, 181-217.
17. Haigh, S. P. 1995 Non-symmetric Holmboe Waves. PhD thesis, University of British Columbia.
18. Hazel, P. 1972 Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39-61.
19. Hecht, J. H., Waltersheid, R. L., Fritts, D. C., Isler, J. R., Senft, D. C., Gardner, C. S. & Franke, S. J. 1997 Wave breaking signatures in OH airglow and sodium densities and temperatures 1. airglow imaging, na lidar, and MF radar observations. J. Geophys. Res. 102, D6, 6655-6668.
20. Hodges, B. R., Imberger, J., Saggio, A. & Winters, K. B. 2000 Modeling basin-scale internal waves in a stratified lake. Limnol. Oceanogr. 45, 1603-1620.
21. Hogg, A. McC. & Ivey, G. N. 2003 The Kelvin-Helmholtz to Holmboe instability transition in stratified exchange flows. J. Fluid Mech. 477, 339-362.
22. Holmboe, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geophys. Publ. 24, 67-113.
23. Holyer, J. Y. 1979 Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433-448.
24. Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509-512.
25. Kelly, R. E. 1965 The stability of an unsteady Kelvin-Helmholtz flow. J. Fluid Mech. 22, 547-560.
26. Klaassen, G. P. & Peltier, W. R. 1985 The onset of turbulence in finite-amplitude Kelvin-Helmholtz billows. J. Fluid Mech. 155, 1-35.
27. Klaassen, G. P. & Peltier, W. R. 1989 Role of transverse secondary instabilities in the evolution of free shear layers. J. Fluid Mech. 202, 367-402.
28. Klaassen, G. P. & Peltier, W. R. 1991 Influence of stratification on secondary instability in free shear layers. J. Fluid Mech. 227, 71-106.
29. Lin, C.-L., Ferziger, J. H. Koseff, J. R. & Monismith, S. G. 1993 Simulation and stability of a two dimensional internal gravity wave in a stratified shear flow. Dyn. Atmos. Oceans 19, 325-366.
30. Lombard, P. N. & Riley, J. J. 1996 Instability and breakdown of internal gravity waves. I. Linear stability analysis Phys. Fluids 8, 3271-3287.
31. Long, R. R. 1972 The steepening of long internal waves. Tellus 24, 88-99.
32. Maslowe, S. A. & Thompson, J. M. 1971 Stability of a stratified free shear layer. Phys. Fluids 14, 453-458.
33. McDougall, T. J. 1979 On the elimination of refractive-index variations in turbulent density-stratified liquid flows. J. Fluid Mech. 93, 83-96.
34. Michallet, H. & Barthelemy, E. 1997 Ultrasonic probes and data processing to study interfacial solitary waves. Exps. Fluids 22, 380-386.
35. Michallet, H. & Ivey, G. N. 1999 'Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104, 13467-13477.
36. Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496-508.
37. Orlanski, I. & Bryan, K. 1969 Formation of the thermocline step structure by large-amplitude internal gravity waves. J. Geophys. Res. 74, 6975-6983.
38. Pawlak, G. & Armi, L. 1996 Stability and mixing of a two-layer exchange flow. Dyn. Atmos. Oceans 139-151.
39. Peltier, W. R. & Caulfield, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135-167.
40. Phillips, O. M. 1966 Dynamics of the Upper Ocean. Cambridge University Press.
41. Ramberg, S. E. & Griffin, O. M. 1987 Laboratory study of steep and breaking deep water waves. J. Waterway, Port, Coast., Ocean Engng 113, 493-506.
42. Scinocca, J. F. 1995 The mixing of mass and momentum by Kelvin-Helmholtz billows. J. Atmos. Sci. 52, 2509-2530.
43. Smyth, W. D., Klaassen, G. P. & Peltier, W. R. 1988 Finite amplitude Holmboe waves. Geophys. Astrophys. Fluid Dyn. 43, 181-222.
44. Smyth, W. D., Moum, J. N. & Caldwell, D. R. 2001 The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations. J. Phys. Oceanogr. 31, 1969-1992.
45. Smyth, W. D. & Winters, K. B. 2003 Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr. 33, 694-711.
46. Smyth, W. D. & Peltier, W. R. 1989 'The transition between Kelvin-Helmholtz and Holmboe instability: An investigation of the overreflection hypothesis. J. Atmos. Sci. 46, 3698-3720.
47. Smyth, W. D. & Peltier, W. R. 1991 Instability and transition in Kelvin-Helmholtz and Holmboe waves. J. Fluid Mech. 228, 387-415.
48. Smyth, W. D. & Peltier, W. R. 1994 Three-dimensionalization of barotropic vortices on the f-plane. J. Fluid Mech. 265, 25-64.
49. Staquet, C. & Sommeria, J. 2002 Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559-593.
50. Stastna, M. & Lamb, K. G. 2002 Large fully nonlinear internal solitary waves: The effect of background current. Phys. Fluids 14, 2897-2999.
51. Stokes, G. G. 1849 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441-455.
52. Thorpe, S. A. 1966 On wave interactions in a stratified fluid. J. Fluid Mech. 24, 737-751.
53. Thorpe, S. A. 1968a A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 693-704.
54. Thorpe, S. A. 1968b On standing internal gravity waves of finite amplitude. J. Fluid Mech. 32, 489-528.
55. Thorpe, S. A. 1968c On the shape of progressive internal waves. Phil. Trans. R. Soc. Lond. A 263, 563-613.
56. Thorpe, S. A. 1971 Experiments on the instability of stratified shear flows: Miscible fluids. J. Fluid Mech. 46, 299-319.
57. Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731-751.
58. Thorpe, S. A. 1975 The excitation, dissipation, and interaction of internal waves in the deep ocean. J. Geophys. Res. 80, 328-338.
59. Thorpe, S. A. 1978 On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech. 85, 7-31.
60. Thorpe, S. A. 1987 Transitional phenomena and the development of turbulence in stratified fluids: A review. J. Geophys. Res. 92, C5, 5231-5248.
61. Troy, C. D. 2003 The breaking and mixing of progressive internal waves. PhD thesis, Stanford University.
62. Troy, C. D. & Koseff, J. R. 2005 The generation and quantitative visualization of breaking internal waves. Exps. Fluids 38, 549-562.
63. Tsuji, Y. & Nagata, Y. 1973 Stokes' expansion of internal deep water waves to the fifth order. J. Oceanogr. Soc. Japan 29, 61-69.
64. Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
65. Wessels, F. & Hutter, K. 1996 Interaction of internal waves with a topographic sill in a two-layered fluid. J. Phys. Oceanogr. 26, 5-20.
66. Winters, K. B. & D'Asaro, E. A. 1994 Three-dimensional wave instability near a critical level. J. Fluid Mech. 272, 255-284.
67. Winters, K. B., Lombard, P. N., Riley, J. J. & D'Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115-128.
68. Woods, J. D. 1968 Wave induced shear instability in summer thermocline. J. Fluid Mech. 32, 791-800.
69. Yau, K.-H., Klaassen, G. P. & Sonmor, L. J. 2004 Principle instabilities of inertio-gravity waves. Phys. Fluids 16, 936-951.