Summary
Two-dimensional free-surface flow about a point vortex in a stream of infinite depth is investigated. The non-linear problem is formulated in terms of an integrodifferential equation on the exact, unknown location of the free surface, and this equation is then solved numerically. The non-linear results are compared with the predictions of linearized theory and, for positive circulation, it is found that the latter may under-estimate the drag force significantly. For negative circulation, the linearized theory grossly over-predicts the value of the wave resistance, which apparently even becomes zero in a limiting configuration.
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Forbes, L.K. On the effects of non-linearity in free-surface flow about a submerged point vortex. J Eng Math 19, 139–155 (1985). https://doi.org/10.1007/BF00042737
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DOI: https://doi.org/10.1007/BF00042737