Abstract
The steady nonlinear free surface flow due to a moving distribution of pressure is considered. Both gravity and surface tension are included in the free surface condition. Numerical solutions are obtained by a boundary integral equation method. Previous investigations have shown that there are solutions with trains of waves in the far field and others with decaying oscillatory tails. In this paper we show that, in the absence of surface tension, there are particular solutions for which waves are trapped under the support of the distribution of pressure. These solutions are related to the “waveless solutions” considered by previous authors. It is shown how these solutions can be used to construct numerically accurate free surface flows which satisfy the radiation condition.
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