The Dynamics of Flat Surface Internal Geophysical Waves with Currents

Abstract

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are presented.

LaTeX, 21 pages, 1 figure, available online in J. Math. Fluid Mech. (2016)

References in corpus (4)

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• Instability of equatorial water waves with an underlying current
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