Standing gravity waves of large amplitude in deep water

Very steep standing gravity waves whose crest accelerations are up to 99.98% of gravity are calculated by developing the method by Tsai and Jeng [Numerical Fourier solutions of standing waves in finite water depth, Appl. Ocean Res. 16 (1994) 185]. The numerical results suggest that the enclosed crest angle of the limiting wave is 90.. The results agree quite well with analytical local solutions for the nearly limiting wave form. We have also found that the standing wave has the maximum wave steepness of 0.6272 when it reaches the limiting profile and that there is a local minimum in the total wave energy as well as a local maximum.