THE SCATTERING OF LONG COASTAL-TRAPPED WAVES IN FRICTIONAL SEAS

The scattering of coastal-trapped waves (CTWs) by a region of irregula r shelf bathymetry is determined from a circulation integral of the de pth-integrated momentum equations. For relatively weak stratification the conservation of geostrophic mass flux along isobaths is used to sh ow that bottom pressure of the transmitted waves is equal to bottom pr essure p(b) of the incident waves, when mapped along constant depth co ntours, plus corrections for the effects of frictional spindown and th e rate of change of relative vorticity. These corrections result from changes in the incident wave alongisobath velocity, which can be ampli fied by the convergence of isobaths between the incident and transmitt ed regions. For the case of the Labrador shelf, the convergence of iso baths 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 geostrophi c mass flux and implies that the frictional correction, while small, i s invalid. However, the transmitted mode 1 and 2 amplitudes determined are insensitive to these corrections and, in agreement with observati ons, are of similar magnitude and about 180 degrees out of phase.