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On the intermediate long wave propagation for internal waves in the presence of currents
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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.
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Modelling intermediate internal waves with currents and variable bottom
A new asymptotic model, the variable-coefficient Intermediate Long Wave Equation, is derived for interfacial waves with shear currents and a slowly varying bottom, with higher-order corrections and a critical-depth condition.
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