Free Surface Waves in Electrohydrodynamics With a Prescribed Vorticity Distribution

ABSTRACT Traditionally, the study of free surface flows assumed irrotationality to simplify matters, and the results seemed to have great success, notably with the Korteweg‐de Vries(KdV) equation. In the past decade, there have been attempts to remove this seemingly strong condition and replace it with a global constant vorticity equivalent to a linear shear flow. In Hunt and Dutykh, a method was developed to deal with not only linear shear flow but with shear flow as a general function of the vertical coordinate. This paper investigates vorticity as a function of and . We demonstrate that our method is versatile enough to cope with this. We use vorticity with a Gaussian profile as an example, but any function can be used. Our method cannot cope with point vortices, but the Gaussian function can be used to approximate a point vortex.