Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation

Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation

The adiabatic decay of different types of internal wave solitons caused by the Earth’s 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’s rotation. The characteristic decay time is derived for different types of solitons for positive and negative coefficients 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 or the asymmetry of solitary waves of opposite polarity. 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’s 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.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 28, 033106 (2018)
and may be found at https://doi.org/10.1063/1.5021864