Abstract
Numerical solutions of irrotational, progressive surface gravity waves in water of a constant depth are obtained by means of an iterative method. Our results suggest that waves with the surface slope angle greater thanπ/6 may exist. The calculated phase velocity of deep water waves near the wave steepness 0.14 is significantly smaller than the value given by the Stokes' fourth approximation.
In order to check our method, we apply it to the problem proposed byDavies (1951), which is hypothetical but similar to the present problem, and for which the exact solution is known. In this case our results show good agreement with the exact solution.
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Sasaki, K., Murakami, T. Irrotational, progressive surface gravity waves near the limiting height. Journal of the Oceanographical Society of Japan 29, 94–105 (1973). https://doi.org/10.1007/BF02109151
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DOI: https://doi.org/10.1007/BF02109151