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.

Keywords

Bibliographic record

BibTeX Citation

@article{Hunt2026freesurface,
  author = {Hunt, M. and Dutykh, D.},
  title = {Free Surface Waves in Electrohydrodynamics With a Prescribed Vorticity Distribution},
  journal = {Math. Methods Appl. Sci.},
  year = {2026},
  volume = {49},
  number = {7},
  pages = {7068--7081},
  doi = {10.1002/mma.70433},
  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.},
  keywords = {free surface waves, electrohydrodynamics, vorticity, water waves, exact solutions},
  publisher = {Wiley},
  issn = {0170-4214}
}