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Gravity currents produced by lock exchange. (English) Zbl 1065.76037

Summary: The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. T. B. Benjamin [J. Fluid Mech. 31, 209–248 (1968; Zbl 0169.28503)] suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of \(\sqrt 2\). New experiments are reported for this case that support the new theoretical value.

MSC:

76B70 Stratification effects in inviscid fluids
76-05 Experimental work for problems pertaining to fluid mechanics

Citations:

Zbl 0169.28503
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