Frictional processes in straits

Abstract

Friction and mixing can be dynamically significant in straits, as in many oceanographic situations. For weak time-dependent homogeneous flows, geostrophy, friction, and acceleration can all play roles in limiting the flow through a strait, and the ratio of the geostrophic elevation difference across the strait to the frictional difference along the strait may be of importance in more general situations. A specific question for quasi-steady exchange flows through straits concerns the influences of friction and entrainment on hydraulic control. Within the context of layered models, these effects tend to drive a flow towards hydraulic criticality in the downstream direction and to shift control points downstream. However, friction and entrainment also induce vertical gradients in velocity and density, rendering layered models dubious. In such situations, the conditions for hydraulic control have been uncertain; even for a homogeneous fluid there is an apparent contradiction between control conditions based on a similarity assumption for the velocity profile on the one hand and on the speed of long waves on the other. The resolution of this contradiction is discussed. It seems that if the frictional forces only involve local flow properties, then inviscid long waves are arrested at the control section (though this is shifted from its location for inviscid flow), but that if flow derivatives along the channel are involved, the condition changes. For a homogeneous flow with shear, internal friction, and bottom friction, the control section is shifted downstream partway to where it would be for a slab flow with bottom friction. While the parameterization of bottom friction actually seems to be reasonably well established, the nature and quantification of internal and lateral frictional processes are uncertain. In a rotating system, secondary cross-strait flows are expected to be driven by the vertical gradient of the vertical Reynolds stress and can provide estimates of the magnitude of bottom and internal friction.