The equilibrium range in the spectrum of wind-generated waves

Consideration of the structure of wind-generated waves when the duration and fetch of the wind are large suggests that the smaller-scale components of the wave field may be in a condition of statistical equilibrium determined by the requirements for attachment of the crests of the waves. A dimensional analysis, based upon the idea of an equilibrium range in the wave spectrum, shows that for large values of the frequency ω, the spectrum Φ (ω) is of the form () g²^-5 where α is an absolute constant. The instantaneous spatial spectrum Ψ (k) is proportional to k −4 for large wave numbers k, which is consistent with the observed occurrence of sharp crests in a well-developed sea, and the loss of energy from the wave system to turbulence and heat is proportional to w u³_*, where ρ w is the water density and u the friction velocity of the wind at the surface. This prediction of the form of Φ (ω) for large ω with α = 7·4×10 −3, agrees well with measurements made by Burling (1955).