Numerical Computation of Large Amplitude Internal Solitary Waves

摘要

Finite amplitude internal solitary waves in a stratified fluid are computed numerically as solutions to a version of Long's equation. Newton's method is used to linearize the two dimensional nonlinear elliptic equation and numerical continuation techniques, both using the wave speed and a pseudo-arclength parameter, are used to trace out solution branches efficiently. Numerical results for the 'tanh' density profile are presented for various depths of the fluid. For shallow depths, solutions for a fixed wave speed are not unique and bore-like solutions with large amplitude have been found. In the deep water case, excellent agreement is obtained with the experimental data of Davis and Acrivos whereas traditional weakly nonlinear analysis fails to produce agreement in the large amplitude regime.