Hamiltonian model for coupled surface and internal waves over currents and uneven bottom

Abstract

A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the Hamiltonian form, and thus the motions of the internal waves and surface waves are determined by the Hamiltonian formulation. Choosing an appropriate scaling of the variables and employing the Hamiltonian perturbation theory from Hamiltonian formulation of the dynamics, we derive a KdV-type equation with variable coefficients depending on the bottom topography to describe the internal waves.

References in corpus (5)

• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
• Hamiltonian model for coupled surface and internal waves in the presence of currents
• Long wave expansions for water waves over random topography
• Hamiltonian approach to modelling interfacial internal waves over variable bottom
• Hamiltonian Approach to Internal Wave-Current Interactions in a Two-Media Fluid with a Rigid Lid