Hamiltonian model for coupled surface and internal waves in the presence of currents

Abstract

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of 'wave' variables and the equations of motion are calculated. The resultant equations of motion are then analysed to show that wave-current interaction is influenced only by the current profile in the 'strips' adjacent to the surface and the interface. Small amplitude and long-wave approximations are also presented.

33 pages, 1 figure

References in corpus (4)

• On an integrable two-component Camassa-Holm shallow water system
• Instability of equatorial water waves with an underlying current
• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
• Hamiltonian Approach to Internal Wave-Current Interactions in a Two-Media Fluid with a Rigid Lid

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• Modelling intermediate internal waves with currents and variable bottom
• Solitary Wave Solution of Flat Surface Internal Geophysical Waves with Vorticity