Equilibrium-range spectrum of waves propagating on currents

By extending the equation proposed in 1981 by Hedges for deepwater spectrum to a finite-depth water, an equation is developed for the equilibrium-range spectrum of waves propagating on a following or opposing current in finite-depth water. To examine the predictability of the developed equation, laboratory experiments were made for the change of Texel, Marsen, and Arsloe (TMA) shallow-water spectra due to currents in water of various depths and current velocities. Comparison with the experimental data shows that the developed equation predicts reasonably well the equilibrium-range spectra of waves propagating on currents. Comparison was also made with the equation originally developed by Kitaigordskii et al. in 1975 and modified later by Gadzhiyev et al. in 1978. A statistical analysis shows that the equation developed in the present study and the equation proposed by Gadzhiyev et al. have essentially the same degree of predictability, both being in reasonable agreement with observations.