Parametric Approach to Wave Forecasting

The prediction of wave characteristics generated by variable winds under fetch- and duration-limited conditions is considered using a parametric approach and a simplified form of the radiative transport equation. The wind-generated sea surface is characterized in terms of an equilibrium range spectrum with a well defined low wave number cut-off. By relating the local wind velocity to the rate of increase in wave energy and incorporating the refractive and frictional effects of transitional water depths into the formulation, governing equations are derived to predict the development of a wind-wave field in terms of integral properties of the spectrum such as mean period, direction, and significant wave height. Under deep water conditions, governing equations admit simple closed form solutions which are shown to compare very favorably with observational data as well as various wind-wave prediction formulae currently available. Consequently, they are numerically solved first for the case of wind-waves in uniform water depth and then for a circular basin with variable bathymetry as an illustrative general case.