ANZIAM J. 42 (E) ppE69--E101, 2001.

A model of weakly vortical interfacial flow

G. A. Jarrad and A. J. Roberts

(Received 31 January 2000)

Abstract

A boundary-integral model is derived to describe two-dimensional, weakly viscous, quasi-irrotational fluid flow at the interface between two fluids. Vortical flow is restricted to a thin boundary layer, allowing the interfacial fluid dynamics to be largely generated by a vortex sheet approximation. A theoretical analysis of the model reveals that small-amplitude interfacial waves have only conservative and dissipative modes of behaviour. In contrast, similar analyses of other models of weak vorticity reveal non-physical modes which increase in energy. Numerical simulations of our model demonstrate the appropriate conservation of key physical invariants.

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Authors

G. A. Jarrad: Dept of Mathematics, University of S.A., Mawson Lakes, South Australia, 5095.
A. J. Roberts: Dept of Maths and Computing, University of Southern Qld, Toowoomba, Queensland, 4350, Australia

Published 22 March 2001.

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Last Modified: Thu Mar 22 12:45:16 2001