Adiabatic decay of internal solitons due to the Earth rotation within the framework of the Gardner-Ostrovsky equation

TL;DR

This paper investigates how Earth's rotation causes internal solitons in the ocean to decay over time, using the Gardner-Ostrovsky equation that includes nonlinear and dispersive effects, and provides estimates relevant to real ocean conditions.

Contribution

It introduces an adiabatic decay model for internal solitons influenced by Earth's rotation within the Gardner-Ostrovsky framework, including decay times for different soliton types.

Findings

Early-stage solitons decay gradually due to Earth's rotation.

Bell-shaped solitons are well-described by adiabatic theory.

Large amplitude table-top solitons are structurally unstable and transform into bell-shaped forms.

Abstract

The adiabatic decay of different types of internal wave solitons caused by the Earth rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth rotation. The characteristic decay time is derived for different types of solitons for positive and negative coefficient of cubic nonlinearity (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity determines only a polarity of solitary wave. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when the cubic nonlinear term is negative, are structurally unstable. Under the influence of Earth rotation they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.