Computations of the almost highest short-crested waves in deep water

The highest short-crested waves have been studied analytically and numerically by several workers, but without a conclusive view. An efficient numerical scheme is proposed in this paper which retains the water-surface elevations in an implicit form in the governing equations, rather than using a series approximation, thus improving the accuracy of the numerical results. Convergence of the numerical scheme is verified. The almost highest short-crested waves in deep water are then evaluated, which are defined for the condition with the largest wave energies. It is found that the critical angle for wave frequency reversal also demarcates the wave characteristics near breaking, for either kinematic or dynamic prominence. The known results available for the limiting two-dimensional cases of standing and progressive waves are compared favourably.