Free Surface Waves in Electrohydrodynamics with Prescribed Vorticity Distribution

Traditionally, the study of free surface flows assumed irrotationality to simplify matters, and the results seemed to have great success, notable 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 global constant vorticity equivalent to a linear shear flow. In [9], 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 x and y . 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. Supplementary Material File (weakly_nonlinear_perscribed_vorticity (2).pdf) - Download - 1.47 MB Information & Authors Information Version history Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record20 Dec 2025Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection

Authors Metrics & Citations Metrics Article Usage 241views 164downloads Citations Download citation M. J. Hunt, Denys Dutykh. Free Surface Waves in Electrohydrodynamics with Prescribed Vorticity Distribution. Authorea. 12 March 2025. DOI: https://doi.org/10.22541/au.174180280.06277609/v1 DOI: https://doi.org/10.22541/au.174180280.06277609/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.