Local bifurcation of electrohydrodynamic waves on a conducting fluid

Zhi Lin School of Mathematical Sciences, Zhejiang University, Zhejiang 310027, China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Zhan Wang Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; School of Engineering Science, University of Chinese Academy Sciences, Beijing 100049, China; Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom

TBD mathscidoc:2204.43021

Physics of Fluids, 29, 032107, 2017.3
We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.
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  title={Local bifurcation of electrohydrodynamic waves on a conducting fluid},
  author={Zhi Lin, Yi Zhu, and Zhan Wang},
  booktitle={Physics of Fluids},
Zhi Lin, Yi Zhu, and Zhan Wang. Local bifurcation of electrohydrodynamic waves on a conducting fluid. 2017. Vol. 29. In Physics of Fluids. pp.032107. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428151109953353149.
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