Capillary-gravity waves on a dielectric fluid of finite depth under normal electric field

Tao Gao, Alex Doak, Jean-Marc Vanden-Broeck, Zhan Wang

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In this work we consider two-dimensional capillary–gravity waves propagating under the influence of a vertical electric field on a dielectric of finite depth bounded above by a perfectly conducting and hydrodynamically passive fluid. Both linear and weakly nonlinear theories are developed, and long-wave model equations are derived based on the analyticity of the Dirichlet–Neumann operator. Fully nonlinear computations are carried out by using a time-dependent conformal mapping method. Solitary waves are found, and their stability characteristics subject to longitudinal perturbations are studied numerically. The shedding of stable solitary waves is achieved by moving a Gaussian pressure on the free surface with the speed close to a phase speed minimum and removing the pressure after a period of time. The novel result shows that a depression bright solitary wave and an elevation generalized solitary wave co-exist in the solitary-wave excitation.
Original languageEnglish
Pages (from-to)98-107
Number of pages10
JournalEuropean Journal of Mechanics, B/Fluids
Early online date20 Jun 2019
Publication statusPublished - 30 Sept 2019


  • Capillary wave
  • Electrohydrodynamics
  • Solitary wave
  • Surface wave

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)


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