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Density Currents in Shear Flows-A Two-Fluid Model

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  • 1 NOAA/ERL, National Severe Storms Laboratory and University of Oklahoma, CIMMS, Norman, Oklahoma
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Abstract

This paper develops a two-fluid steady-state model of a density current and its front propagating into a uniformly sheared environmental flow. This model is used to examine the kinematic and dynamic factors that control the depth and propagation speed of the density current and the geometric shape of the density current front. For an idealized inviscid flow, the results show that the density current becomes deeper and propagates faster relative to the environmental flow as the shear increases toward positive (i.e., the system-relative inflow speed decreases with height). When the effects of energy loss and negative vorticity generation are taken into account for the entire or physically constrained fractional depth of the upper-layer outflow, multiple solutions are found for two possible flow states: supercritical and subcritical, similar to that of Benjamin. The supercritical (or subcritical) state is characterized by a large (small) Froude number for the downstream upper-layer outflow, in which case the density current is shallower (or much shallower) and propagates slightly faster (or significantly slower) than the idealized inviscid one. The depth and propagation speed of a density current of supercritical (or subcritical) state increase rapidly (or decrease very slowly) as the shear increases toward positive, but change very slightly (or significantly) with the energy loss and/or negative vorticity generation. Applications of the model results to real atmospheric density currents are also discussed.

Abstract

This paper develops a two-fluid steady-state model of a density current and its front propagating into a uniformly sheared environmental flow. This model is used to examine the kinematic and dynamic factors that control the depth and propagation speed of the density current and the geometric shape of the density current front. For an idealized inviscid flow, the results show that the density current becomes deeper and propagates faster relative to the environmental flow as the shear increases toward positive (i.e., the system-relative inflow speed decreases with height). When the effects of energy loss and negative vorticity generation are taken into account for the entire or physically constrained fractional depth of the upper-layer outflow, multiple solutions are found for two possible flow states: supercritical and subcritical, similar to that of Benjamin. The supercritical (or subcritical) state is characterized by a large (small) Froude number for the downstream upper-layer outflow, in which case the density current is shallower (or much shallower) and propagates slightly faster (or significantly slower) than the idealized inviscid one. The depth and propagation speed of a density current of supercritical (or subcritical) state increase rapidly (or decrease very slowly) as the shear increases toward positive, but change very slightly (or significantly) with the energy loss and/or negative vorticity generation. Applications of the model results to real atmospheric density currents are also discussed.

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