Free surfaces, wave motion oscillations

Develop an analysis for surface wave motion of a liquid having a finite depth H. Show that for wavelengths comparable in magnitude to H or larger, an oscillating boundary layer develops at the sohd surface in the low viscosity limit and the time factor p is given for a free surface by... 

Above this value, oscillations induced on the free surface are stable, while below this value, it is possible to induce instability on the surface and form droplets. Viscosity caimot prevent the instability, but it does increase the acceleration necessary to cause the instability to appear. In the equation of motion (6), acceleration due to gravity, g, also acts to stabilize the interface. There are different ways to destabilize the surface, the simplest of which is to i/>(f) to a constant value above g + dipiAjK), forming a gravity wave. Other ways include harmonic excitation with where i = W is the ampli-... 

In summary, harbor oscillations arise through co-oscillation of sea surface elevations and currents in the harbor with those at the entrance to the harbor. Seichegenerating motions outside the harbor typically have periods of several minutes and most commonly arise from bound and free long waves that are incident on the harbor entrance. 

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