Internal solitary waves in a linearly stratified fluid

Abstract

The mode shapes for internal solitary waves propagating in a linearly stratified fluid of finite depth are determined in the limit of weak stratification. The solutions obtained for both a fixed upper boundary and a free surface are compared with known results for exponential stratification. The profound changes which occur depending on whether the upper surface is fixed or free are derived from the strong influence of the free surface when the stratification is weak. Evidence is presented supporting the conjecture that the free surface can no longer effect qualitative differences in the modal structure when the fluid is heavily stratified.