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arXiv · 2506.10123

Modelling intermediate internal waves with currents and variable bottom

Rossen Ivanov·Lyudmila Ivanova
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Abstract

A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet-Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin-Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well.

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Rossen Ivanov, Lyudmila Ivanova. 2025-06-11. Modelling intermediate internal waves with currents and variable bottom. https://doi.org/10.1016/j.nonrwa.2025.104451

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