The superharmonic instability of Stokes waves in deep water

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Abstract
The method of Tanaka (1983) is used to solve the eigenvalue problem determining the form of the first superharmonic instability of periodic Stokes waves. Comparisons are made with other approaches to this problem and a discussion of the advantages of Tanaka's method is given. The accurately resolved eigenfunction solution is then taken as the initial state for commencing the computational time-stepping method of Dold & Peregrine (1985), by which we investigate the full nonlinear development of the growing and decaying modes of this instability. It is observed that all unstable modes develop to breaking in the periodic regime and this result is compared and contrasted with the solitary wave case.

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