Hamiltonian approach to modelling interfacial internal waves over variable bottom

Abstract

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave-current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV-mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton fission, which is analysed and studied numerically as well.

arXiv commentLaTeX, 37 pages, 7 figures

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Cited by in corpus (8)

• Higher-order integrable models for oceanic internal wave-current interactions
• Nonlinear two-dimensional water waves with arbitrary vorticity
• Modulational instability of nonuniformly damped, broad-banded waves: applications to waves in sea-ice
• Hamiltonian model for coupled surface and internal waves over currents and uneven bottom
• Modelling intermediate internal waves with currents and variable bottom
• An introduction to the Zakharov equation for modelling deep water waves
• Benjamin-Ono dynamics of internal waves with currents
• Three-layer water flows: Dirichlet-Neumann operators and approximations