Free-surface flows under gravity and surface tension effects due to pressure distribution

Abstract

We consider steady two-dimensional free surface flows due to an applied pressure distribution under the effects of both gravity and surface tension in water of a constant depth. The fluid is assumed to be inviscid and incompressible and the flow is irrotational. The behavior of nonlinear waves is characterized by three parameters: the Froude number, F, the Bond number, tau, and the magnitude and sign of the pressure distribution, epsilon. The nonlinear wave problem was solved numerically by a boundary integral method. In addition, we studied some aspects of linear and weakly nonlinear theories in the case of small of amplitude wave to establish connections with the nonlinear solutions. It was found that, when tau > 1/3, the appropriate model for the weakly nonlinear theory is the fKdV equation whereas the fNLS equation gives better description of the wave form solution in the case when tau < 1/3. In general, we found that, when F and tau given, thereexist both elevation and depression waves. Also a new family of nonlinear waves in the form of multi-mode waves was demonstrated.