On the intermediate long wave propagation for internal waves in the presence of currents

Abstract

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are presented as well.

29 pages, 1 figure

References in corpus (3)

• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
• Hamiltonian model for coupled surface and internal waves in the presence of currents
• Hamiltonian Approach to Internal Wave-Current Interactions in a Two-Media Fluid with a Rigid Lid

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• The Lagrangian formulation for wave motion with a shear current and surface tension
• Modelling surface waves on shear current with quadratic depth-dependence
• Hamiltonian model for coupled surface and internal waves over currents and uneven bottom
• Modelling intermediate internal waves with currents and variable bottom
• Benjamin-Ono dynamics of internal waves with currents