Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 370, Issue 1, Pages 1-48Publisher
SPRINGER
DOI: 10.1007/s00220-019-03483-8
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Funding
- University of Vienna
- WWTF research Grant [MA16-009]
- EPSRC [EP/K032208/1]
- Isaac Newton Institute for Mathematical Sciences, Cambridge
- EPSRC [EP/K032208/1] Funding Source: UKRI
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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.
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