Dynamics of fully nonlinear capillary-gravity solitary waves under normal electric fields.

Two-dimensional capillary-gravity waves travelling under the effect of a vertical electric field are considered. The fluid is assumed to be a dielectric of infinite depth. It is bounded above by another fluid which is hydrodynamically passive and perfectly conducting. The problem is solved numerically by time-dependent conformal mapping methods. Fully nonlinear waves are presented, and their stability and dynamics are studied.

On asymmetric generalized solitary gravity-capillary waves in finite depth.

Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented.

Forced solitary waves and fronts past submerged obstacles.

Herein, an efficient numerical method is presented to describe the flow of a liquid in an open channel with various types of bottom configurations. The method is developed for steady two-dimensional potential free surface flows. The resulting nonlinear problem is solved numerically by boundary integral equation methods. In addition weakly nonlinear solutions are derived. New solutions which complement those of Dias and Vanden-Broeck [J. Fluid Mech. 59, 93-102 (2004)] are presented. Furthermore some solutions for channel flows past dips in the bottom are discussed.