Integrable Models of Internal Gravity Water Waves Beneath a Flat Surface

Alan Compelli, Rossen Ivanov, Tony Lyons

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.
Original languageEnglish (Ireland)
Title of host publicationNonlinear Water Waves
Subtitle of host publicationAn Interdisciplinary Interface
Publication statusPublished - Nov 2019

Publication series

NameTutorials, Schools, and Workshops in the Mathematical Sciences


  • Internal waves, Currents, Nonlinear waves, Long waves, Hamiltonian Systems, Solitons


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