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

摘要

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 #x201C;bright#x201D; and #x201C;dark#x201D; 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.