Rossby Wave Scattering by a Meridional Line Barrier in an Infinitely Long Zonal Channel

Abstract

The interaction of a prescribed channel mode Rossby wave with a meridional line barrier situated in an infinitely long, zonally aligned channel is considered. An analytical solution for the scattered field is presented for a barrier that spans half the channel width. The solution is obtained using the Wiener-Hopf technique. For other barrier widths the scattered field is determined by numerically solving the Rossby wave equation. In all cases the scattered field is described in terms of propagating cross-channel eigenmodes, together with an infinite number of evanescent modes. The solutions are interpreted in terms of the energy density and energy flux associated with each scattered field eigenmode. Mode one dominates the energy balance in the scattered field for most barrier widths in response to a mode-one incident wave. However, for a particular range of barrier widths the second cross-channel mode is found to be the most energetic. The energy density of each scattered field mode is larger on the eastern side of the barrier than on the west. The implication of the model results for Rossby wave propagation in the Southern Ocean are examined.