COMPUTATIONS OF STEEP GRAVITY-WAVES BY A REFINEMENT OF DAVIES-TULINS APPROXIMATION

Water waves in water of arbitrary depth and solitary saves are calculated numerically using new series truncation methods. The techniques use a refinement of Davies' approximation first proposed by Tulin. Accurate numerical solutions are obtained for all values of the steepness up to the limiting configuration with a 120 degrees angle at the wave crest. It is shown that the proposed numerical procedure is equivalent to the method of Havelock. The method of Michell is included as a particular case. A comparison with previous numerical methods, such as boundary integral equation techniques, is given.