A new translating quasigeostrophic V-state

Abstract

A new nonlinear translating V-state of the barotropic quasigeostrophic equations with topography in the form of an infinitely long escarpment (or step) is computed numerically. Before the numerical computation, with the assumption of small excursions by fluid columns across the step, the linear equations of motion are solved analytically, demonstrating the possibility of constructing a translating V-state. The linear V-state has zero total circulation and self-propagates parallel to the step. It consists of two line vortices with positive circulation located on the deep side of the step and a finite-area patch of constant negative vorticity on the shallow side comprising of fluid which has crossed the step from the deep side. The linear solution motivates the numerical search for a nonlinear translating V-state comprising of two line vortices and a finite-area patch of constant vorticity. An algorithm based on contour dynamics and Newton's method is used to find such a V-state. Time-dependent contour dynamics is used to compute the evolution of the V-state and it is found to be unstable. However, the growth rate of disturbances is sufficiently small for the V-state to survive several turn-over times.