Modelling intermediate internal waves with currents and variable bottom

Abstract

A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet-Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin-Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well.

23 pages, 2 figures

References in corpus (10)

• Hamiltonian model for coupled surface and internal waves in the presence of currents
• The Dynamics of Flat Surface Internal Geophysical Waves with Currents
• On the intermediate long wave propagation for internal waves in the presence of currents
• Hamiltonian approach to modelling interfacial internal waves over variable bottom
• Surface waves over currents and uneven bottom
• On the dynamics of internal waves interacting with the equatorial undercurrent
• Benjamin-Ono model of an internal wave under a flat surface
• Hamiltonian description of internal ocean waves with Coriolis force
• Higher-order integrable models for oceanic internal wave-current interactions
• The Lagrangian formulation for wave motion with a shear current and surface tension