Edwards, C. and Howison, S. D. and Ockendon, H. and Ockendon, J. R. (2007) Nonclassical shallow water flows. IMA Journal of Applied Mathematics . (In Press)

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Abstract
This paper deals with violent discontinuities in shallow water flows with large Froude number .
On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity may be described by a deltashock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step functioncomponents. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted.
For flows on a sloping base, we show that for flow with an aspect ratio of () on a base with an or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a deltashock. The physical manifestation of this discontinuity is a small `tube' of fluid bounding the flow. The deltashock conditions for this flow are derived and solved for a point source on an inclined plane. This latter deltashock framework also sheds light on the evolution of the layer impact on a horizontal base.
Item Type:  Article 

Uncontrolled Keywords:  deltashock, jet impact, hypercritical flow 
Subjects:  O  Z > Partial differential equations D  G > Fluid mechanics 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  578 
Deposited By:  Sam Howison 
Deposited On:  21 Mar 2007 
Last Modified:  29 May 2015 18:24 
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