Shear-induced breaking of large internal solitary waves

Journal of Fluid Mechanics

Volumn 620, Issue , 2009, Pages 1-29

  Fructus, Dorian ^a   Carr, Magda ^b   Grue, John ^a   Jensen, Atle ^a   Davies, Peter A ^c  

^a UNIVERSITY OF OSLO   (Norway)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

^c UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

HORIZONTAL WELLS; OCEANOGRAPHY; SOLITONS; STABILITY; VELOCITY MEASUREMENT;

HORIZONTAL VELOCITY; INDUCED VELOCITY; INTERNAL SOLITARY WAVES; PARTICLE IMAGE VELOCIMETRIES; PROPAGATION SPEED; RICHARDSON NUMBER; STABILITY PROPERTIES; STEADY SHEAR FLOW;

SHEAR FLOW;

INTERNAL WAVE; RICHARDSON NUMBER; SHEAR FLOW; SOLITARY WAVE; VELOCITY PROFILE; WAVELENGTH;

EID: 65649121586     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008004898     Document Type: Article

References (34)

1. ALEXAKIS, A. 2005 On Holmboe's instability for smooth shear and density profiles. Phys. Fluids 17, 84-103.
2. BOGUCKI, D. & GARRETT, C. 1993 A simple model for the shear-induced decay of an internal solitary wave. J. Phys. Oceanogr. 23, 1767-1776.
3. CARPENTER, J. R., LAWRENCE, G. A., & SMYTH, W. D. 2007 Evolution and mixing of asymmetric Holmboe instabilities. J. Fluid Mech. 582, 103-132.
4. CARR, M., FRUCTUS, D., GRUE, J., JENSEN, A. & DAVIES, P. A. 2008 Convectively-induced shear instability in large internal solitary waves. Phys. Fluids 20, 12660.
5. CAULFIELD, C. P. & PELTIER, W. R. 2000 Three dimensionalization of the stratified mixing layer. Phys. Fluid 413, 1-47.
6. DALZIEL, S. B. 2006 Digiflow user guide. http://www.dampt.cam.ac.uk/lab/digiflow/.
7. DUDA, T. F., LYNCH, J. F., IRISH, J. D., BEARDSLEY, R. C. & RAMP, S. R. 2004 Internal tide and nonlinear wave behaviour in the continental slope in the northern South China Sea. IEEE J. Ocean Engng 29 1105-31.
8. FRINGER, O. B. & STREET, R. L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494, 319-353.
9. FRUCTUS, D. & GRUE, J. 2004 Fully nonlinear solitary waves in a layered stratified fluid. J. Fluid Mech. 505, 323-347.
10. GARDNER, C. S., GREENE, J. M., KRUSKAL, M. D. & MUIRA, R. M. 1967 Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19, 1095-1097.
11. GRUE, J. 2005 Generation, propagation, and breaking of internal solitary waves. Chaos 15, 037110-1-14.
12. GRUE, J. 2006 Very large internal waves in the ocean - observations and nonlinear models. In Waves in Geophysical Fluids - Tsunamis, Rogue Waves, Internal Waves and Internal Tides (ed. J. Grue & K. Trulsen), pp. 205-270. Springer.
13. GRUE, J., JENSEN, A., RUSÅS, P.-O. & SVEEN, J. K. 1999 Properties of large-amplitude internal waves. J. Fluid Mech. 380, 257-278.
14. HAZEL, P. 1972 Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39-61.
15. HELFRICH, K. R. & MELVILLE, W. K. 2006 Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38, 395-425.
16. HOGG, A. M. & IVEY, G. N. 2003 The Kelvin-Helmholtz to Holmboe instability transition in stratified exchange flows. J. Fluid Mech. 477, 339-362.
17. HOLMBOE, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geophys. Publ. 24, 67-112.
18. HOWARD, L. N. 1961 Note on a paper by John W. Miles. J. Fluid Mech. 10, 509-512.
19. KAO, T. W., PAN, F.-S. & RENOUARD, D. 1985 Internal solitons on the pycnocline: Generation, propagation, and shoaling and breaking over a slope. J. Fluid Mech. 159:19-53.
20. MICHALLET, H. & BARTÉLEMY 1998 Experimental study of interfacial solitary waves. J. Fluid Mech. 366, 159-177.
21. MILES, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496-508.
22. MOUM, J. N., FARMER, D. M., SMYTH, W. D., ARMI, L. & VAGLE, S. 2003 Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward over the continental shelf. J. Phys. Oceanogr. 33, 2093-2112.
23. OSTROVSKY, L. A. & GRUE, J. 2003 Evolution equations for strongly nonlinear internal waves. Phys. Fluids 15 (10), 2934-2948.
24. OSTROVSKY, L. A. & STEPANYANTS, Y. A. 2005 Internal solitons in laboratory experiments. Chaos 15, 037111-1-28.
25. PELTIER, W. R. & CAULFIELD, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135-167.
26. SCOTTI, R. S. & CORCOS, G. M. 1972 An experiment on the stability of small disturbances in a stratified free shear layer. J. Fluid Mech. 52, 499-528.
27. SMYTH, W. D., NASH, J. D. & MOUM, J. N. 2005 Differential diffusion in breaking Kelvin-Helmholtz billows. J. Phys. Oceanogr. 35, 1004-1022.
28. STANTON, T. P. & OSTROVSKY, L. A. 1998 Observations of highly nonlinear internal solitons over the continental shelf. Geophys. Res. Lett. 25 (14), 2695-2698.
29. STAQUET, C. 2000 Mixing in a stably stratified shear layer: Two- and three-dimensional numerical experiments. Fluid Dyn. Res. 27 367-404.
30. SVEEN, J. K., GUO & GRUE, J. 2002 On the breaking of internal solitary waves at a ridge. J. Fluid Mech. 469, 161-188.
31. TROY, C. D. & KOSEFF, J. R. 2005 The instability and breaking of long internal waves. J. Fluid Mech. 543, 107-136.
32. TUNG, K.-K., CHAN, T. F. & KUBOTA, T. 1982 Large amplitude internal waves of permanent form. Stud. Appl. Math. 66, 1-44.
33. TURKINGTON, B., EYDELAND, A. & WANG, S. 1991 A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Math. 85, 93-127.
34. ZHU, D. Z. & LAWRENCE, G. A. 2001 Holmboe's instability in exchange flows. J. Fluid Mech. 429, 391-409.