Abstract
Fourth order evolution equations have been derived for three-dimensional Stokes waves on arbitrary water depth. In deep water the equations reduce to those of Dysthe, and on finite depth the third order terms agree with those of Benney and Roskes, Hasimoto and Ono and Davey and Stewartson. The results of the stability analysis for uniform waves based on the new arbitrary depth expressions are superior to those based on the finite depth approximation and they agree fairly well with the exact calculations of McLean. It is demonstrated that dimensionless water depth as well as wave steepness influences the applicability of the deep water stability expressions.
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