The Scattering of Long Coastal-Trapped Waves in Frictional Seas

Abstract

The scattering of coastal-trapped waves (CTWs) by a region of irregular shelf bathymetry is determined from a circulation integral of the depth-integrated momentum equations. For relatively weak stratification the conservation of geostrophic mass flux along isobaths is used to show that bottom pressure of the transmitted waves is equal to bottom pressure pb of the incident waves, when mapped along constant depth contours, plus corrections for the effects of frictional spindown and the rate of change of relative vorticity. These corrections result from changes in the incident wave alongisobath velocity, which can be amplified by the convergence of isobaths between the incident and transmitted regions. For the case of the Labrador shelf, the convergence of isobaths south of the (incident) Hudson Strait region leads to a tenfold increase in the production of relative vorticity and in the correction for pressure for a mode 1 incident wave. This leading order increase in vorticity production violates the assumption of constant geostrophic mass flux and implies that the frictional correction, while small, is invalid. However, the transmitted mode 1 and 2 amplitudes determined are insensitive to these corrections and, in agreement with observations, are of similar magnitude and about 180° out of phase.