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.

This paper concerns the interaction between solitary waves on the surface of an ideal fluid and a localized external force, which models a moving disturbance on the free surface or an obstacle moving at the bottom of a channel. Previous works have investigated this interaction under the assumption that the external force moves with variable speed and constant acceleration. However, in this paper we adopt a different approach and consider the scenario in which the external force moves with variable speed and non-constant acceleration. Using the Whitham equation framework, we investigate numerically trapped waves excited by a periodic external force. Our experiments reveal regimes in which solitary waves are spontaneously generated and trapped for large times at the external force. In addition, we compare the results predicted by the Whitham equation with those of the Korteweg–de Vries equation.

Non-stationary, rotational, linear surface waves are considered where the underlying sheared current has constant vorticity. A time-dependent study is presented on the formation and persistence of a Kelvin cat-eye structure in the presence of bottom topography. The flow domain is two-dimensional, which allows for the use of a conformal mapping and working in a computational flat-bottom domain. In some cases an initial disturbance is prescribed, while in others the waves are generated from rest. Submarine particle dynamics numerically captures the horizontal critical layer, defined by closed orbits separating the fluid domain into two disjoint regions. In the wave’s moving frame, these recirculation regions are structured in the form of Kelvin cat-eyes. Owing to the interaction with topography, the usual travelling-wave formulation is abandoned and the critical layer is identified through a non-stationary set of equations. The respective time-dependent Kelvin cat-eye structure dynamically adjusts itself at the onset of wave–topography interaction, without losing its integrity. The formation of a Kelvin cat-eye structure is also studied in the case where the surface is initially undisturbed. Surface waves are generated from either the current–topography interaction or by a pressure distribution suddenly imposed along the free surface. Under the pressure forcing, an isolated cat-eye forms with a single recirculation region beneath the wave.