Skip to main content Accessibility help

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

  • Karl R. Helfrich (a1)


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.



Hide All
Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559592.
Cacchione, D. A. & Southard, J. B. 1974 Incipient sediment movement by shoaling internal gravity waves. J. Geophys. Res. 79, 22372242.
Cacchione, D. A. & Wunsch, C. 1974 Experimental study of internal waves over a slope. J. Fluid Mech. 66, 223239.
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, 591599.
Davis, R. E. & Acrivos, A. 1967 Solitary internal waves in deep water. J. Fluid Mech. 29, 593607.
Djordjevic, V. D. & Redekopp, L. G. 1978 The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr. 8. 10161024.
Fu, L. L. & Holt, B. 1982 Seasat views oceans and sea ice with synthetic aperture radar. JPL Publications, pp. 81120. Feb. 15.
Haury, L. R., Briscoe, M. G. & Orr, M. H. 1978 Tidally generated internal wave packets in the Massachusetts Bay. Nature 278, 312317.
Helfrich, K. R. & Melville, W. K. 1986 On long nonlinear internal waves over slope—shelf topography. J. Fluid Mech. 167, 285308 (referred to herein as HM).
Helfrich, K. R., Melville, W. K. & Miles, J. W. 1984 On interfacial solitary waves over slowly varying topography. J. Fluid Mech. 149, 305317.
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, 650658.
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479500.
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, 1953.
Knickerbocker, C. J. & Newell, A. C. 1980 Internal solitary waves near a turning point. Phys. Lett. 75A, 326330.
Osborne, A. R. & Burch, T. L. 1980 Internal solitons in the Andaman Sea. Science 208, 451459.
Philips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep Sea Res. 17, 435443.
Sandstrom, H. & Elliott, J. A. 1984 Internal tide and solitons on the Scotian Shelf: a nutrient pump at work. J. Geophys. Res. 89, 64156426.
Segur, H. & Hammack, J. L. 1982 Soliton models of long internal waves. J. Fluid Mech. 118, 285304.
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, 419442 (referred to herein as WW).
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

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

  • Karl R. Helfrich (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.