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Internal solitary wave breaking and run-up on a uniform slope

Published online by Cambridge University Press:  26 April 2006

Karl R. Helfrich
Karl R. Helfrich
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole. MA 02543. USA
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Abstract

Laboratory experiments have been conducted to study the shoaling of internal solitary waves of depression in a two-layer system on a uniform slope. The shoaling of a single solitary wave results in wave breaking and the production of multiple turbulent surges, or boluses, which propagate up the slope. Significant vertical mixing occurs everywhere inshore of the breaking location. The kinematics of the breaking and bolus runup are described and a breaking criterion is found. The energetics of the breaking are investigated. Over the range of parameters examined, 15 (±5) % of the energy lost from first-mode wave motion inshore of the break point goes into vertical mixing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 133 - 154
Copyright
© 1992 Cambridge University Press

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References

Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559–592.Google Scholar
Cacchione, D. A. & Southard, J. B. 1974 Incipient sediment movement by shoaling internal gravity waves. J. Geophys. Res. 79, 2237–2242.Google Scholar
Cacchione, D. A. & Wunsch, C. 1974 Experimental study of internal waves over a slope. J. Fluid Mech. 66, 223–239.Google Scholar
Chapman, D. C., Geise, G. S., Collins, M. G., Encarnacion, R. & Jacinto, G. 1991 Evidence of internal swash associated with Sulu Sea Solitary waves? Cont. Shelf Res. 11, 591–599.Google Scholar
Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29, 593–607.Google Scholar
Djordjevic, V. D. & Redekopp, L. G. 1978 The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr. 8. 1016–1024.Google Scholar
Fu, L. L. & Holt, B. 1982 Seasat views oceans and sea ice with synthetic aperture radar. JPL Publications, pp. 81–120. Feb. 15.
Haury, L. R., Briscoe, M. G. & Orr, M. H. 1978 Tidally generated internal wave packets in the Massachusetts Bay. Nature 278, 312–317.Google Scholar
Helfrich, K. R. & Melville, W. K. 1986 On long nonlinear internal waves over slope—shelf topography. J. Fluid Mech. 167, 285–308 (referred to herein as HM).Google Scholar
Helfrich, K. R., Melville, W. K. & Miles, J. W. 1984 On interfacial solitary waves over slowly varying topography. J. Fluid Mech. 149, 305–317.Google Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature of turbulence in a stratified fluid. Part 1. The energetics of mixing. J. Phys. Oceanogr. 21, 650–658.Google Scholar
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479–500.Google Scholar
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. 169, 19–53.Google Scholar
Knickerbocker, C. J. & Newell, A. C. 1980 Internal solitary waves near a turning point. Phys. Lett. 75A, 326–330.Google Scholar
Osborne, A. R. & Burch, T. L. 1980 Internal solitons in the Andaman Sea. Science 208, 451–459.Google Scholar
Philips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep Sea Res. 17, 435–443.Google Scholar
Sandstrom, H. & Elliott, J. A. 1984 Internal tide and solitons on the Scotian Shelf: a nutrient pump at work. J. Geophys. Res. 89, 6415–6426.Google Scholar
Segur, H. & Hammack, J. L. 1982 Soliton models of long internal waves. J. Fluid Mech. 118, 285–304.Google Scholar
Wallace, B. C. & Wilkinson, D. L. 1988 Run-up of internal waves on a gentle slope in a two-layered system. J. Fluid Mech. 191, 419–442 (referred to herein as WW).Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.