La auto-interacción alineal de un modo normal de Rossby en un océano rectangular

Abstract

The self-interaction of a rossby normal mode in a rectangular basin is studied by means of an analytical and a numerical model. The analytical approach is based on perturbation methods. At first order in the nonlinearties, the self-interaction produces a steady forcing and a transient forcing oscillating at twice the frequency of the mode. Both the steady and the transient forcing can never be resonant. the response to the steady forcing has an anticyclonic gyre in the northern half of the basin and a cyclonic one in the southern half. The direct response to the trasient forcing does not satisfy the boundary condition of no normal flow at the meridional walls. The fluid then adjusts by generating free Rossby waves (homogeneous solution) to balance out the forced flow normal to the walls. Among the components of the perturbative solution at first order, the steady solution is the most important one. The advective terms in the QG potential vorticity equation play an important role in the circulation of the basin if this relatively small; on the contrary, for the relatively big basins nonlinear terms are not important.

For small amplitudes, the numerical solution agreess with the analytical solution, except for a delay in the period, i.e. the period of the numerical solution in the slightly larger (order 10% for the cases run here) than the period of  the analytical solution. This is presumably due to the effect of the discretization in the numerical model which leads to a difference between the anlytical and numerical frequency of a Rossby wave. The solution to first order differs apprecibly from numerical solution as the amplitude of the normal mode (initial condition) is increased, indicating that the analytical solution is valid for small  β-Rossby numbers