# American Institute of Mathematical Sciences

August  2019, 39(8): 4519-4532. doi: 10.3934/dcds.2019185

## Benjamin-Ono model of an internal wave under a flat surface

 1 School of Mathematical Sciences, University College Cork, Cork, Ireland 2 School of Mathematical Sciences, Technological University Dublin, City Campus, Kevin Street, Dublin 8, Ireland

The paper is for the special theme: Mathematical Aspects of Physical Oceanography, organized by Adrian Constantin.

Received  August 2018 Revised  October 2018 Published  May 2019

Fund Project: This work was supported by EPSRC grant no EP/K032208/1. AC is also funded by SFI grant 13/CDA/2117

A two-layer fluid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a flat surface. The fluids are incompressible and inviscid. A Hamiltonian formulation for the dynamics in the presence of a depth-varying current is presented and it is shown that an appropriate scaling leads to the integrable Benjamin-Ono equation.

Citation: Alan Compelli, Rossen Ivanov. Benjamin-Ono model of an internal wave under a flat surface. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4519-4532. doi: 10.3934/dcds.2019185
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