On the barotropic discharge of a homogeneous fluid onto a continental shelf

Abstract

Strong flow from a river or estuary onto a gently sloping continental shelf is a commonly occurring geophysical phenomenon. As a very simple model for this phenomenon, we consider the steady discharge of a homogeneous fluid onto a rotating, two-dimensional continental shelf with constant bottom slope (and a rigid top surface). The flow is barotropic, and bottom friction is the principal dissipation mechanism. Both steady state and time-dependent numerical models were developed to examine the dependence of the structure of the flow over the shelf on the strength of the river discharge. The numerical results indicate that for weakly nonlinear flow, vortex stretching due to the offshore motion of the river discharge is balanced by bottom friction and the jet turns sharply to the right (facing offshore at the river mouth in the northern hemisphere), in agreement with the arrested topographic wave solutions given by Csanady (1979, Journal of Physical Oceanography, 8, 47–62) and Beardsley and Hart (1978, Journal of Geophysical Research, 83, 873–883). As the river discharge is increased, advection tends to conserve the cyclonic vorticity induced by topographic stretching, so the jet is advected offshore to the left, slowing down and turning to the right. The results of several simple laboratory experiments indicate that for even stronger discharge, the jet separates into a cyclonic and an anticyclonic eddy, on the left and the right of the jet, respectively, before being entrained into a sequence of rightward moving eddies. When considered together, the numerical and laboratory experiments suggest that an increasing discharge causes a transition from a weakly nonlinear steady flow regime, to a highly structured, strongly nonlinear flow field with time-dependent eddy formation.