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IMA Journal of Applied Mathematics 2003 68(6):665-686; doi:10.1093/imamat/68.6.665
© 2003 by Institute of Mathematics and its Applications
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Dynamics of a two-layer fluid sloshing problem

D. Mackey1 and E. A. Cox2

1 School of Mathematics, Dublin City University, Dublin 9, Ireland 2 Department of Mathematical Physics, University College, Dublin 4, Ireland

A second-order ordinary differential equation, which is a reduced form of the periodically forced extended Korteweg–de Vries (eKdV) equation, is derived in the physical context of sloshing a two-layer fluid tank. In the limit of small dispersion, numerical evidence is given of multiple periodic solutions displaying fast oscillations superimposed on slow periodic waves and a higher-order Melnikov method is then used to verify the existence of such solutions. The dynamical behaviour of a similar equation with more general coefficients is also examined, demonstrating the existence of periodic and chaotic behaviour. We highlight new aspects which arise due to the presence of mixed nonlinearity.

Keywords: chaos; Melnikov methods; mixed nonlinearity; periodic solutions; sloshing; two-layer flow.

Received 11 November 2002.


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