Fetch-Limited Growth of Wind Waves in Deep Water

摘要

The existing wind wave growth formulas (WWGFs) in form of power function are analyzed. It is shown that these WWGFs after eliminating the fetch are uniformly consistent with the 3/2 power law, although originally there are considerable discrepancy among them. It is found that the similarity of integrals of the three wind input parameterizations exists by analogy. Likewise it is found that the similarity of integrals of the three dissipation parameterizations exists by analogy. The fractional fetch power law for wind wave growth in deep water is presented by combining the energy balance equation for significant wave with the similarities of wind input and dissipation parameterizations, after invoking the 3/2 power law. The semi-empirical WWGFs have been proposed by fitting the existing WWGFs with the derived fetch law. The proposed formulas are agreeably consistent with the available observational data.