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A free boundary problem arising in a model for shallow water entry at small deadrise angles

Published online by Cambridge University Press:  03 May 2005

S. D. HOWISON  and
J. M. OLIVER
S. D. HOWISON
Affiliation:
Mathmatical Institute, 24 - 29 St. Giles', Oxford OX1 3LB, UK email: howison@maths.ox.ac.uk
J. M. OLIVER
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
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Abstract

A free boundary problem arising in a model for inviscid, incompressible shallow water entry at small deadrise angles is derived and analysed. The relationship between this novel free boundary problem and the well-known viscous squeeze film problem is described. An inverse method is used to construct explicit solutions for certain body profiles and to find criteria under which the splash sheet can ‘split’. A variational inequality formulation, conservation of certain generalized moments and the Schwarz function formulation are introduced.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 6 , December 2004 , pp. 839 - 851
Copyright
2004 Cambridge University Press

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