Rotating gravity current and channel flows

Abstract

A theoretical and laboratory Investigation of rotating gravity currents and channel flows is presented. The study is applicable to buoyancy driven flows through straits, mid ocean ridge valleys and fracture zones, and intermittent gravity currents. In the theoretical study two extensions are achieved to the energy conserving theory of Hacker (1996). Hacker considered three flow geometries, case A - weak rotation, case B - intermediate rotation and case C - strong rotation. Firstly, the theory is extended to include dissipation. This is achieved in a similar manner to that used by Benjamin (1968) to include energy loss in the non-rotating gravity current theory. The governing equations and numerical solutions for the three flow geometries are presented. For shallow currents the energy loss theory predicts that the Froude number tends to 2* irrespective of the rotation rate. For deeper currents the Froude number increases with rotation. The second extension to the energy conserving theory is the inclusion of an upstream potential vorticity boundary conditionin the current. The approach taken is based on a method used by van Heijst (1985). The governing equations and preliminary solutions for each case are derived. The potential vorticity theory provides an insight into the circulation that develops within the current.However, varying the pre-set potential vorticity in the source region does not appear to have a significant effect upon the front speed and the other principle variables.In the laboratory investigation the effects of fractional depth and rotation rate on the velocity and other parameters which characterise the flow are quantified. For weakly rotating currents, w/R < 0.7 (where w is the width of the channel and R the Rossby radius), the measured front speed is in fair agreement with the energy loss and potential vorticity theories. At higher rotation rates the front speed is lower than predicted. However, the theories assume that the fluid is inviscid, the no-slip condition is not applied at the boundary, potential vorticity is conserved and that energy loss is uniform across the channel. The theory does not include factors such as the enhanced vertical mixing and the development of a geostrophic eddy. These are associated with strong rotation rates and could account for the divergence of the experimental results from the theory.

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