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Large mode-2 internal solitary waves in three-layer flows

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Internal waves are commonly observed in the world’s oceans and are of great importance in physical oceanography. It is estimated that 90% of the kinetic energy associated with oceanic internal waves is contained within the first two baroclinic modes. While extensive experimental and mathematical research into mode-1 waves exists, there are very limited studies into mode-2 waves, despite the increasing recognition of their importance. In this talk we shall discuss mode-2 large amplitude internal solitary waves in a three-layer configuration, bounded above and below by a rigid wall. We will start by considering a strongly nonlinear model that extends the two-layer Miyata-Choi-Camassa (MCC) model. Its solitary-wave solutions are governed by a Hamiltonian system with two degrees of freedom, and revealed by Barros et al. (2020) to have several strongly nonlinear characteristics that fail to be captured by the existing weakly nonlinear theory. In addition to large amplitude mode-2 waves with single-hump profiles, new classes of mode-2 solutions, characterised by multi-humped wave profiles of large amplitude, are also found. The rationale behind the existence of such waves is explained based on the asymptotic limit when the density transition layer is thin. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the full dynamical system. Then, we will move to the fully nonlinear theory of Euler equations and compare the solutions obtained for the two models. These share the same conjugate states corresponding to potential front solutions and a good agreement of solutions is expected. Although, as we will show, regimes can be identified where even though the long-wave approximation appears valid, certain features of solutions only match qualitatively.

This talk is part of the Isaac Newton Institute Seminar Series series.

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