Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields

M. V. Flamarion, E. Kochurin () and R. Ribeiro-Jr
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M. V. Flamarion: Unidade Acadêmica do Cabo de Santo Agostinho, UFRPE/Rural Federal University of Pernambuco, BR 101 Sul, Cabo de Santo Agostinho 54503-900, PE, Brazil
E. Kochurin: Institute of Electrophysics, Ural Branch of Russian Academy of Sciences, Yekaterinburg 620016, Russia
R. Ribeiro-Jr: Departamento de Matemática, Centro Politécnico, UFPR/Federal University of Paraná, Jardim das Américas, Caixa Postal 19081, Curitiba 81531-980, PR, Brazil

Mathematics, 2023, vol. 11, issue 21, 1-13

Abstract: This work presents the results of a direct numerical simulation of the nonlinear free surface evolution of a finite-depth fluid with a linear shear flow under the action of horizontal electric fields. The method of time-dependent conformal transformation for the description of the combined effects of the electric fields and constant vorticity is generalized for the first time. The simulation results show that strong shear flow co-directed in the wave propagation direction leads to the formation of large-amplitude surface waves, and, for some limiting vorticity value, a wave breaking process with the formation of an air bubble in the liquid is possible. The oppositely directed shear flow can cause the retrograde motion of a surface wave (wave propagation in the opposite direction to the linear wave speed). The simulations conducted taking into account the electro-hydrodynamic effects demonstrate that a high enough external horizontal electric field suppresses these strongly nonlinear processes, and the surface waves tend to preserve their shape.

Keywords: shear flow; conformal transformation; nonlinear waves; free surface; electric field; direct numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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