The influence of a narrow transverse canyon on initially geostrophic flow

Abstract

The interaction of a geostrophic current with a transverse submarine canyon is considered with an analytical, two‐level model of a homogeneous fluid on an f plane. The dynamical hypothesis is that the flow in the canyon is forced by the pressure gradient due to a sloping free surface. The interaction of flow in the canyon with the overlying fluid is through the vertical velocity forced by divergence in the canyon. The mathematical problem considers a flat‐bottom ocean with an infinitely long canyon having a rectangular cross section and uniform depth. The dynamics are rotationally modified, shallow‐water equations for each level. The initial time behavior of the model is considered with a power series solution which shows that flow in the canyon responds quickly, in about 0.1 of the inertia period, to an imposed surface pressure gradient. The time‐dependent model is solved by means of a Laplace transform in time in three spatial domains: over the canyon and on either side. For a canyon of arbitrary width, the flow over the canyon is composed of standing waves, while radiating waves exist on either side of the canyon. In the absence of friction, the oscillations continue indefinitely, since there are standing gravity modes in the canyon. In steady state, there is no net flow of water across the canyon, so such submarine features should act as barriers to barotropic geostrophic flow. The limit of a narrow canyon is considered. Arguments are presented to show that a canyon is narrow if its width is less than half of the smaller of the radius of deformation or the width scale of the overlying current. For a forcing current with a width about equal to the radius of deformation, the oscillations in the canyon have periods of about 0.1 up to 1. times the inertia period. Such oscillations have been observed in most canyons for which current meter observations exist.