Equatorial Wave–Current Interactions

By Adrian Constantin, Rossen I. Ivanov. Communications in Mathematical Physics, 2019

150 citations recorded by the source corpus.

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 regime. In particular, specific weakly nonlinear long-wave regimes capture the wave-breaking phenomenon while others are structure-enhancing since therein the dynamics is described by an integrable Hamiltonian system whose solitary-wave solutions are solitons.

Subfields: Atmospheric Science, Oceanography

View Paper: https://www.semanticscholar.org/paper/e394e45737cc814f37f5f606fc178d288b4981cc