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.

arXiv comment29 pages, 1 figure

References in corpus (7)

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• Hamiltonian model for coupled surface and internal waves in the presence of currents
• The Dynamics of Flat Surface Internal Geophysical Waves with Currents
• 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 Approach to Internal Wave-Current Interactions in a Two-Media Fluid with a Rigid Lid

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• Higher-order integrable models for oceanic internal wave-current interactions
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• On the modelling of short and intermediate water waves
• 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