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.
Benjamin-Ono model of an internal wave under a flat surface
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abstract
A two-layer fluid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a flat surface. The fluids are incompressible and inviscid. A Hamiltonian formulation for the fluid dynamics is presented and it is shown that an appropriate scaling leads to the integrable Benjamin-Ono equation.
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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.