ACCURATE CALCULATIONS OF STOKES WATER-WAVES OF LARGE-AMPLITUDE

This paper reports on a detailed study of large amplitude gravity waves of the Stokes type on deep water, in which a combination of analytical work, carried out with the help of symbolic computation, and accurate numerical work performed on a supercomputer was used. Strong numerical evidence is presented showing that the Stokes method of calculation, as well as its more recent computer extensions, are questionable for intermediate to large amplitude waves. In particular, the resulting Stokes representation of the coordinates x and y as double series in the stream function-psi and velocity potential-phi appear to diverge. In contrast, it is shown that the direct formulation recently introduced by Hui and Tenti, in which y = y(x, psi), produces a series representation so well behaved that-accurate results for all the wave properties can be obtained with relatively low order partial sums.