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Conservation law modelling of entrainment in layered hydrostatic flows

Published online by Cambridge University Press:  05 May 2015

Paul A. Milewski  and
Esteban G. Tabak
Paul A. Milewski*
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
Esteban G. Tabak
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA
*
†Email address for correspondence: p.a.milewski@bath.ac.uk
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Abstract

A methodology is developed for modelling entrainment in two-layer shallow water flows using non-standard conserved quantities, replacing layerwise mass conservation by global energy conservation. Thus, the energy that the standard model would regularly dissipate at internal shocks is instead available to exchange fluid between the layers. Two models are considered for the upper boundary of the flow: a rigid lid and a free surface. The latter provides a selection principle for choosing physically relevant conservation laws among the infinitely many that the former possesses, when the ratio between the baroclinic and barotropic speeds tends to zero. Solutions of the equations are studied analytically and numerically, applied to the lock-exchange problem, and compared with other closures.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 272 - 294
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Copyright
© 2015 Cambridge University Press 

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