STANDING GRAVITY WAVES OF FINITE AMPLITUDE IN LIQUID OF INFINITE DEPTH

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Abstract
In this paper, standing gravity waves of finite amplitude on the surface of an incompressible inviscid liquid of infinite depth are considered. The motion is taken to be two-dimensional, irrotational and time-periodic. An infinite series solution, in terms of a wave parameter, is assumed for the complex potential and a comparatively simple process is developed for obtaining each successive term. This process differs from the one proposed in an earlier investigation by Penney and Price (1). It appears that certain apparently arbitrary terms arising in this earlier investigation may in fact be determined by ensuring that the solution is time-periodic.

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