Error Calculation of Large-Amplitude Internal Solitary Waves Within the Pycnocline Introduced by the Strong Stratification Approximation

Abstract

At present, studies on large-amplitude internal solitary waves mostly adopt strong stratification models, such as the two-and three-layer Miyata—Choi—Camassa (MCC) internal wave models, which omit the pycnocline or treat it as another fluid layer with a constant density. Because the pycnocline exists in real oceans and cannot be omitted sometimes, the computational error of a large-amplitude internal solitary wave within the pycnocline introduced by the strong stratification approximation is unclear. In this study, the two- and three-layer MCC internal wave models are used to calculate the wave profile and wave speed of large-amplitude internal solitary waves. By comparing these results with the results provided by the Dubreil—Jacotin—Long (DJL) equation, which accurately describes large-amplitude internal solitary waves in a continuous density stratification, the computational errors of large-amplitude internal solitary waves at different pycnocline depths introduced by the strong stratification approximation are assessed. Although the pycnocline thicknesses are relatively large (accounting for 8%–10% of the total water depth), the error is much smaller under the three-layer approximation than under the two-layer approximation.

Keywords

Internal solitary wave / Pycnocline / Two-layer approximation / Three-layer approximation / MCC internal wave model / DJL equation / Wave profile / Wave speed