A model for wave growth in fetch-limited conditions

In this paper,it is held that the universal relationships of wave growth in fetch-limited conditions,i.e.,f_p=Ax^-B and m₀=Cx^D should satisfy the Toba 3/2 power law and the wave energy balance equation.In the ideal generation situation,theoretically it can be derived that the ideal fetch-limited wave growth relationship should have D=3B and D+B=1,(i.e.,B=0.25,D=0.75) and A³C=2.1×10^-4C_d^1/2,where C_d is the drag coefficient.The 3/2 power law,the wave energy balance equation and the decrease of wave steepness with increasing fetch have became three requirements which should be satisfied by fetch-limited wave growth algorithms.A semi-empirical and semi-theoretical model for fetch-limited wave growth is presented.In the application to the slanting wind situation an universal relationship of dimensionless wave energy vs dimensionless peak frequency is presented and the comparisons show that the model is in good agreement with observations.