Jf. Middleton et Ma. Merrifield, THE SCATTERING OF LONG COASTAL-TRAPPED WAVES IN FRICTIONAL SEAS, Journal of physical oceanography, 25(4), 1995, pp. 502-512
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.