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The Dynamics of Flat Surface Internal Geophysical Waves with Currents

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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.

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  1. School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

    Alan Compelli & Rossen I. Ivanov

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  1. Alan Compelli
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  2. Rossen I. Ivanov
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Correspondence to Rossen I. Ivanov.

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Communicated by A. Constantin

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Compelli, A., Ivanov, R.I. The Dynamics of Flat Surface Internal Geophysical Waves with Currents. J. Math. Fluid Mech. 19, 329–344 (2017). https://doi.org/10.1007/s00021-016-0283-4

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