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Nonlinear progressive free waves in a circular basin

A nonlinear analysis is presented of waves propagating around the free surface of water contained in a circular basin of finite uniform depth. The property that distinguishes these waves from unidirectional gravity waves is the occurrence of low-order resonant interactions between the components composing them. Steady waves in the neighbourhood of resonance are calculated in the fully nonlinear problem, when it is shown that multiple families of free-wave solutions, each family having a different set of resonating wave components, are associated with each of the water depths at which resonance occurs. Linear stability calculations indicate that most steady waves dominated by resonating wave components are linearly unstable. The nonlinear time evolution of perturbed waves is calculated as a check on the linear stability results, leading to doubts about the relevance of the linear prediction when marginal instability is said to occur.