Conservation law modelling of entrainment in layered hydrostatic flows

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 availab...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 772; pp. 272 - 294
Main Authors Milewski, Paul A., Tabak, Esteban G.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 10.06.2015
Subjects
Computer based modeling
Conservation
Conservation laws
Energy conservation
Entrainment
Fluid mechanics
Free surfaces
Shallow water
Water flow
internal waves
shallow water flows
wave breaking
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2015.210