Journal
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
Volume 19, Issue 4, Pages 237-252Publisher
SPRINGER
DOI: 10.1007/s00162-005-0163-7
Keywords
depression wave; elevation wave; trapped bubble; KdV; gravity-capillary
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We consider steady free surface two-dimensional flow due to a localized applied pressure distribution under the effects of both gravity and surface tension in water of constant depth, and in the presence of a uniform stream. The fluid is assumed to be inviscid and incompressible, and the flow is irrotational. The behavior of the forced nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, tau > 1/3, and the magnitude and sign of the pressure forcing parameter epsilon. The fully nonlinear wave problem is solved numerically by using a boundary integral method. For small amplitude waves and F < 1 but not too close to 1, linear theory gives a good prediction for the numerical solution of the nonlinear problem in the case of bifurcation from the uniform flow. As F approaches 1, the nonlinear terms need to be taken account of. In this case the forced Korteweg-de Vries equation is found to be an appropriate model to describe bifurcations from an unforced solitary wave. In general, it is found that for given values of F < 1 and tau > 1/3, there exists both elevation and depression waves. In some cases, a limiting configuration in the form of a trapped bubble occurs in the depression wave solutions.
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