Abstract

An extension to the energy-conserving theory of gravity currents in rectangular rotating channels is presented, in which an upstream potential vorticity boundary condition in the current is applied. It is assumed that the fluid is inviscid; that the Boussinesq approximation applies; that the fundamental properties of momentum, energy, volume flux and potential vorticity are conserved between upstream and downstream locations; and that the flow is dissipationless. The upstream potential vorticity in the current is set through the introduction of a new parameter at the right-hand wall at high rotation rates. The introduction of the potential vorticity boundary condition into the energy-conserving theory does not appear to have a substantial effect on the main flow parameters (such as current speed and width); however it does provide an insight into the complex dynamics of the flow within the current.

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