On long nonlinear internal waves over slope-shelf topography

TLDR

The study investigates the propagation and stability of long nonlinear internal waves over slope–shelf topography. The authors formulate and numerically solve a generalized KdV equation that incorporates nonlinearity, dispersion, dissipation, and variable bottom topography, and validate it with laboratory experiments in a salt‑stratified system. The model agrees well with experiments across various stratifications, topographies, and wave amplitudes, but omitting dissipation and cubic nonlinearity leads to significant discrepancies; observed weak shearing and strong breaking instabilities depend on wave amplitude and shelf stratification, and the lowest‑mode instability can spawn a second‑mode solitary wave, informing field data interpretation.

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.