Periodic, finite‐amplitude, axisymmetric gravity waves

A study is made of finite-amplitude axisymmetric gravity waves in a circular basin of uniform depth. Periodic, free, first-mode oscillations of a nonviscous incompressible liquid are considered. Through the use of Dini expansions, the exact nonlinear governing equations are solved by an iterative procedure which has been carried through the third approximation. The effects of finite amplitude on the surface profile and on the frequency of oscillation are investigated, and the amplitude and angle at the crest of a maximum wave are studied. It is noted that at certain ‘critical’ depth-radius ratios the first-mode oscillation may be coupled with a higher-mode motion at an integral multiple of the basic frequency.