Implications of an f−4 Equilibrium Range for Wind-Generated Waves

Abstract

The existence of an f?5 equilibrium range was hypothesized for middle to high frequencies for a well-developed sea generated by the physical parameters of gross sea state in the pioneering work of Phillips. Various experimental studies since then, notably JONSWAP, have shown that if the power law is ?5, then the proportionality constant is frequency dependent. Recent Lake Ontario data has shown an f?4 variation, which agrees with models of the equilibrium range as a Kolmogorov cascade. From this, the JONSWAP fetch relation and appropriate Assumptions about momentum transfer are shown to imply an important new spectra form for energy transfer from wind to wave, which differs slightly from other recent attempts. With suitable parameter relations, the midrange spectral energy can be shown to be essentially the same as its well known f?5 counterpart.