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Gravity currents entering a two-layer fluid

Published online by Cambridge University Press:  19 April 2006

Judith Y. Holyer  and
Herbert E. Huppert
Judith Y. Holyer
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: Topexpress, Ltd. 1 Portugal Place, Cambridge.
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

This paper presents a study of steady gravity currents entering a two-layer system, with the current travelling either along the boundary to form a boundary current, or between the two different layers to form an intrusion. It is shown that, at the front of an intrusion, the streamlines meet at angles of 120° at a stagnation point. For an energy-conserving current the volume inflow rate to the current, the velocity of propagation and the downstream depths are determined. In contrast to the pioneering study of Benjamin (1968), it is found that the depth of the current is not always uniquely determined and it is necessary to use some principle additional to the conservation relationships to determine which solution occurs. An appropriate principle is obtained by considering dissipative currents. In general, if the volume inflow rate to a current is prescribed, the current loses energy in order to maintain a momentum balance. We thus suggest the criterion that the energy dissipation is a maximum for a fixed volume inflow rate. It is postulated that the energy which is lost will go to form a stationary wave train behind the current. A nonlinear calculation is carried out to determine the amplitude and wavelength of these waves for intrusions. Such waves have been observed on intrusions in laboratory experiments and the results of the calculation are found to agree well with the experiments. Similar waves have not been observed on boundary currents because the resulting waves have too much energy and break.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 4 , 29 October 1980 , pp. 739 - 767
Copyright
© 1980 Cambridge University Press

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