Author(s)

L. J. Campbell

Abstract

This paper examines the nonlinear dynamics of a Rossby wave propagating longitudinally in a north-south shear flow. The flow configuration is an idealized model for a western boundary current in an ocean basin. It is assumed that there is a critical layer in the flow, where the shear flow speed is the same as the wave phase speed. The nonlinear critical-layer evolution of the wave depends on the direction of propagation of the wave. Numerical simulations show that an eastwardpropagating wave incident on the critical layer from the west is absorbed by the mean flow at early times. This is the same situation that is known to occur for small-amplitude waves, according to the linear theory. At later times, however, nonlinear waves may be reflected from the critical layer. In contrast, a westwardpropagatingwave incident on the critical layer from the east passes through largely unaffected. An approximate analytic solution of the linearized equations is also presented to give further insight into the evolution of the critical layer. Keywords: critical layer, Rossby waves, nonlinear wave interactions, western boundary current, shear flow, numerical simulations. 1 Introduction An idealized model for the dynamics of Rossby waves in a western boundary current in an ocean basin consists of a latitudinally-periodicRossby wave propagating horizontally in the zonal direction in a north-south shear flow [6, 7, 8]. This paper examines the nonlinear interactions between the waves and the current in the vicinity of a critical layer. A critical layer is a region surrounding a longitude at which the shear flow velocity is equal to the phase speed of the wave.When the governing linearized inviscid equations are solved numerically or analytically it is seen that

Keywords

critical layer, Rossby waves, nonlinear wave interactions, western boundary current, shear flow, numerical simulations.