Internal waves occur within a fluid that is density-stratified, most commonly by temperature or salinity variation. In the oceans, such disturbances in internal layers are often generated by tides. They appear as large amplitude, long wavelength nonlinear waves and can propagate over large distances. Photographs taken from orbital shuttle as well as local measurements show that their presence has a significant effect on the surface of the ocean. In some instances, the visible signature of internal waves on the surface of the ocean is a band of roughness which propagates at the same velocity as the internal wave, followed after its passage, by the mill pond effect, the complete calmness of the sea. I will show an asymptotic analysis and a derivation of an effective system of PDEs modeling the coupling between the interface and the free surface of a two layers fluid in a scaling regime chosen to capture these observations.

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