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Internal solitons on the pycnocline: generation, propagation, and shoaling and breaking over a slope

Published online by Cambridge University Press:  20 April 2006

Timothy W. Kao ,
Fuh-Shing Pan  and
Dominique Renouard
Timothy W. Kao
Affiliation:
Department of Civil Engineering, The Catholic University of America, Washington, D.C. 20064
Fuh-Shing Pan
Affiliation:
Department of Civil Engineering, The Catholic University of America, Washington, D.C. 20064
Dominique Renouard
Affiliation:
Department of Civil Engineering, The Catholic University of America, Washington, D.C. 20064 Permanent address: Institut de Mécanique de Grenoble, France.
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Abstract

In Part 1 a study is made of the internal solitary wave on the pycnocline of a continuously stratified fluid. A Korteweg–de Vries (KdV) equation for the ‘interfacial’ displacement is developed following Benney's method for long nonlinear waves. Experiments were conducted in a long wave tank with the pycnocline at several different depths below the free surface, while keeping the total depth approximately constant. A step-like pool of light water, trapped behind a sliding gate, served as the initial disturbance condition. The number of solitons generated was verified to satisfy the prediction of inverse-scattering theory. The fully developed soliton was found to satisfy the KdV theory for all ratios of upper-layer thickness to total depth.

In Part 2 of this study we investigate experimentally the evolution and breaking of an internal solitary wave as it shoals on a sloping bottom connecting the deeper region where the waves were generated to a shallower shelf region. It is found through quantitative measurements that the onset of wave-breaking was governed by shear instability, which was initiated when the local gradient Richardson number became less than ¼. The internal solitary wave of depression was found to steepen at the back of the wave before breaking, in contrast with waves of elevation. Two slopes were used, with ratios 1:16 and 1:9, and the fluid was a Boussinesq fluid with weak stratification using brine solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 19 - 53
Copyright
© 1985 Cambridge University Press

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