Hamiltonian formulation for water waves over a variable bottom: Asymptotic models and numerical simulations

@inproceedings{Craig2009HamiltonianFF,
  title={Hamiltonian formulation for water waves over a variable bottom: Asymptotic models and numerical simulations},
  author={Walter Craig and Philippe Guyenne and Catherine Sulem},
  year={2009}
}
We present a Hamiltonian, potential-flow formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to a lower-dimensional system involving boundary variables alone. To accomplish this, we express the Dirichlet–Neumann operator as a Taylor series in terms of the surface and bottom variations. This expansion is convenient for both asymptotic calculations and direct numerical simulations. First, we apply this… CONTINUE READING

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