Journal of Fluid Mechanics

On long nonlinear internal waves over slope-shelf topography

Karl R.  Helfrich a1p1 and W. K.  Melville a1
a1 R. M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Article author query
helfrich kr   [Google Scholar] 
melville wk   [Google Scholar] 


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.

(Published Online April 21 2006)
(Received March 29 1985)
(Revised December 16 1985)

p1 Present address: Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.

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