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.
| Original language | English |
|---|---|
| Pages (from-to) | 272-294 |
| Number of pages | 23 |
| Journal | Journal of Fluid Mechanics |
| Volume | 772 |
| DOIs | |
| Publication status | Published - 1 Jun 2015 |
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Keywords
- internal waves
- shallow water flows
- wave breaking
Cite this
Conservation law modelling of entrainment in layered hydrostatic flows. / Milewski, Paul A.; Tabak, Esteban G.
In: Journal of Fluid Mechanics, Vol. 772, 01.06.2015, p. 272-294.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Conservation law modelling of entrainment in layered hydrostatic flows
AU - Milewski, Paul A.
AU - Tabak, Esteban G.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
KW - internal waves
KW - shallow water flows
KW - wave breaking
UR - http://www.scopus.com/inward/record.url?scp=84929192369&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1017/jfm.2015.210
U2 - 10.1017/jfm.2015.210
DO - 10.1017/jfm.2015.210
M3 - Article
VL - 772
SP - 272
EP - 294
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -