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Full-Text Articles in Physical Sciences and Mathematics
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Articles
We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Articles
We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.
Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov
Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov
Articles
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system. The …