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Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution
Version 1
: Received: 4 November 2019 / Approved: 6 November 2019 / Online: 6 November 2019 (11:33:50 CET)
Version 2 : Received: 14 April 2020 / Approved: 15 April 2020 / Online: 15 April 2020 (10:05:39 CEST)
Version 2 : Received: 14 April 2020 / Approved: 15 April 2020 / Online: 15 April 2020 (10:05:39 CEST)
How to cite: Hunt, M.; Dutykh, D. Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution. Preprints 2019, 2019110062. https://doi.org/10.20944/preprints201911.0062.v1 Hunt, M.; Dutykh, D. Free Surface Flows in Electrohydrodynamics with a Constant Vorticity Distribution. Preprints 2019, 2019110062. https://doi.org/10.20944/preprints201911.0062.v1
Abstract
In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed.
Keywords
electro-hydrodynamics; constant vorticity; Burns condition; weakly nonlinear analysis
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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