Surface waves over currents and uneven bottom
arXiv:1811.03140 · doi:10.1016/j.dsr2.2018.11.004
Abstract
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth. Emergence of new solitons is observed as a result of the wave interaction with the uneven bottom.
arXiv comment17 pages, LaTeX, 7 figures
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Cited by in corpus (9)
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- On the intermediate long wave propagation for internal waves in the presence of currents
- Oblique interactions between solitons and mean flows in the Kadomtsev-Petviashvili equation
- Hamiltonian approach to modelling interfacial internal waves over variable bottom
- Nonlinear two-dimensional water waves with arbitrary vorticity
- The Lagrangian formulation for wave motion with a shear current and surface tension
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