a b s t r a c tIn this work we consider two-dimensional capillary-gravity waves propagating under the influence of a vertical electric field on a dielectric of finite depth bounded above by a perfectly conducting and hydrodynamically passive fluid. Both linear and weakly nonlinear theories are developed, and long-wave model equations are derived based on the analyticity of the Dirichlet-Neumann operator. Fully nonlinear computations are carried out by using a time-dependent conformal mapping method. Solitary waves are found, and their stability characteristics subject to longitudinal perturbations are studied numerically. The shedding of stable solitary waves is achieved by moving a Gaussian pressure on the free surface with the speed close to a phase speed minimum and removing the pressure after a period of time. The novel result shows that a depression bright solitary wave and an elevation generalized solitary wave co-exist in the solitary-wave excitation.

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. Coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of steady periodic traveling waves with constant vorticity on a dielectric fluid under the effect of normal electric fields. Through the conformal mapping technique combined with pseudo-spectral numerical methods, we develop an approach that allows us to conclude that the flow can have zero, two, or three stagnation points according to variations in the voltage potential. We describe in detail the recirculation zones that emerge together with the stagnation points. In addition, we show that the number of local maxima of the pressure on the bottom boundary is intrinsically connected to the saddle points.

A finite difference scheme is proposed to solve the problem of axisymmetric Taylor bubbles rising at a constant velocity in a tube. A method to remove singularities from the numerical scheme is presented, allowing accurate computation of the bubbles with the inclusion of both gravity and surface tension. This paper confirms the long-held belief that the solution space of the axisymmetric Taylor bubble for small surface tension is qualitatively similar to that of the plane Taylor bubble. Furthermore, evidence suggesting that the solution selection mechanism associated with plane bubbles also occurs in the axisymmetric case is presented.

We consider a potential flow model of axisymmetric waves travelling on a ferrofluid jet. The ferrofluid coats a copper wire, through which an electric current is run. The induced azimuthal magnetic field magnetises the ferrofluid, which in turn stabilises the well known Plateau–Rayleigh instability seen in axisymmetric capillary jets. This model is of interest because the stabilising mechanism allows for axisymmetric magnetohydrodynamical solitary waves. A numerical scheme capable of computing steady periodic, solitary and generalised solitary wave solutions is presented. It is found that the solution space for the model is very similar to that of the classical problem of two-dimensional gravity–capillary waves.

Nonlinear free surface flows past a disturbance in a channel of finite depth are considered. The fluid is assumed to be incompressible and inviscid and the flow to be two-dimensional, irrotational and supercritical. The disturbance is chosen to be a point vortex. Highly accurate numerical solutions are computed. The basic idea of the numerical approach is first to develop codes to compute solitary waves and then to introduce appropriate modifications to model the point vortex. Previous results are recovered and new solutions are presented.