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Circulation based models for Boussinesq gravity currents
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In addition to the conservation of mass and horizontal momentum, existing analytical models of gravity currents traditionally require an assumption about the conservation or loss of energy along specific streamlines for closure. Here, we show that the front velocity of gravity currents can be predicted as a function of their height from mass and momentum balances alone by considering the evolution of interfacial vorticity. This approach does not require information on the pressure field and therefore avoids the need for the energy conservation arguments invoked by earlier models. Predictions by the new theory are shown to be in close agreement with results from numerical simulations. We also discuss the influence of downstream mixing on the front velocity predicted by this theory.
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