Integrable Models of Internal Gravity Water Waves Beneath a Flat Surface
A two-layer fluid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is bounded below by a flat bottom and the upper layer is bounded above by a flat surface. The fluids are incompressible and inviscid and Coriolis forces as well as currents are taken into consideration. A Hamiltonian formulation is presented and appropriate scaling leads to a KdV approximation. Additionally, considering the lower layer to be infinitely deep leads to a Benjamin–Ono approximation.
KeywordsInternal waves Currents Nonlinear waves Long waves Hamiltonian systems Solitons
Mathematics Subject Classification (2000)Primary: 35Q35 35Q51 35Q53; Secondary: 37K10
The authors are grateful to the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), Vienna (Austria) for the opportunity to participate in the workshop Nonlinear Water Waves—an Interdisciplinary Interface, 2017 where a significant part of this work has been accomplished. AC is also funded by SFI grant 13/CDA/2117.
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