Finite-amplitude perturbations and modulational instability of a stable geostrophic front

Abstract

The finite-amplitude evolution of neutral perturbations to the Cushman-Roisin frontal geostrophic model for a simple upwelling front with spatially varying potential vorticity is determined. It is shown that the sinuous and varicose modes are governed by the “bright” and “dark” NLS equations, respectively. This implies that the sinuous modes can exhibit Benjamin-Feir instability (while the varicose modes do not), suggesting the possibility that envelope solitons can form on a frontal outcropping. Exploiting the underlying Hamiltonian structure, it is nevertheless shown that all monotomc parallel front solutions of the Cushman-Roisin model are nonlinearly stable in the sense of Liapunov.