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Applied mathematics, Fluids and plasma physics
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.
Compelli, A.,Ivanov, R. & Lyons, T. (2020) Nonlinear Water Waves: an Interdisciplinary Interface, Springer Nature, Switzerland. isbn:978-3-030-33536-6