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On long nonlinear internal waves over slope-shelf topography

Published online by Cambridge University Press:  21 April 2006

Karl R. Helfrich  and
W. K. Melville
Karl R. Helfrich
Affiliation:
R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.
W. K. Melville
Affiliation:
R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

An experimental and theoretical study of the propagation and stability of long nonlinear internal waves over slope–shelf topography is presented. A generalized Korteweg–de Vries (KdV) equation, including the effects of nonlinearity, dispersion, dissipation and varying bottom topography, is formulated and solved numerically for single and rank-ordered pairs of solitary waves incident on the slope. The results of corresponding laboratory experiments in a salt-stratified system are reported. Very good agreement between theory and experiment is obtained for a range of stratifications, topography and incident-wave amplitudes. Significant disagreement is found in some cases if the effects of dissipation and higher-order (cubic) nonlinearity are not included in the theoretical model. Weak shearing and strong breaking (overturning) instabilities are observed and found to depend strongly on the incident-wave amplitude and the stratification on the shelf. In some cases the instability of the lowest-mode wave leads to the generation of a second-mode solitary wave. The application of these findings to the prediction and interpretation of field data is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 285 - 308
Copyright
© 1986 Cambridge University Press

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