Abstract

In the weakly nonlinear long-wave régime, internal solitary waves are often modelled by the Korteweg–de Vries equation, which is well known to support an exact solitary wave solution. However, when the effect of background rotation is taken into account, an additional term is needed and the outcome is the Ostrovsky equation. Although the additional term would appear to be relatively mild, being a linear long-wave perturbation, it has the drastic effect of destroying the solitary wave solution. Instead an initial solitary-like disturbance decays into radiating oscillatory waves, with the eventual formation of a nonlinear envelope wave packet, whose carrier wavenumber is determined by an extremum in the group velocity. In this paper, we will use a combination of theoretical analyses, numerical simulations and laboratory experiments to describe this process.

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