Formation of Regions with High Energy and Pressure Gradients at the Free Surface of Liquid Dielectric in a Tangential Electric Field

  • E. A. Kochurin


The nonlinear dynamics of the free surface of an ideal incompressible non-conducting fluid with a high dielectric constant subjected to a strong horizontal electric field is simulated using the method of conformal transformations. It is shown that in the initial stage of interaction of counter-propagating periodic waves of significant amplitude, there is a direct energy cascade leading to energy transfer to small scales. This results in the formation of regions with a steep wave front at the fluid surface, in which the dynamic pressure and the pressure exerted by the electric field undergo a discontinuity. It has been demonstrated that the formation of regions with high gradients of the electric field and fluid velocity is accompanied by breaking of surface waves; the boundary inclination angle tends to 90◦, and the surface curvature increases without bound.


free surface nonlinear waves electric field electrohydrodynamics wave breaking liquid dielectrics 


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  1. 1.
    J. R. Melcher and W. J. Schwarz, “Interfacial Relaxation Overstability in a Tangential Electric Field,” Phys. Fluids 11, 2604–2616 (1968).CrossRefADSGoogle Scholar
  2. 2.
    L. L. Barannyk, D. T. Papageorgiou, and P. G. Petropoulos, “Suppression of Rayleigh–Taylor Instability Using Electric Fields,” Math. Comput. Simulat. 82, 1008–1016 (2012).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    M. F. El-Sayed, “Electro-Aerodynamic Instability of a Thin Dielectric Liquid Sheet Sprayed with an Air Stream,” Phys. Rev. E 60, 7588–7591 (1999).CrossRefADSGoogle Scholar
  4. 4.
    N. M. Zubarev and O. V. Zubareva, “Nondispersive Propagation of Waves with Finite Amplitudes on the Surface of Dielectric Liquid in a Tangential Electric Field,” Pis’ma Zh. Tekh. Fiz. 32 (200), 40–44 (2006).Google Scholar
  5. 5.
    N. M. Zubarev and E. A. Kochurin, “Three-Dimensional Nonlinear Waves at the Interface between Dielectric Fluids in an External Horizontal Electric Field,” Prikl. Mekh. Tekh. Fiz. 54 (2), 52–58 (2013) [J. Appl. Mech. Tech. Phys. 54 (2), 212–217 (2013)].MathSciNetMATHGoogle Scholar
  6. 6.
    N. M. Zubarev and E. A. Kochurin, “The Interaction of Strongly Nonlinear Waves on the Free Surface a Non-Conducting Fluid in a Horizontal Electric Field,” Pis’ma Zh. Eksp. Teor. Fiz. 99 (11), 729–734 (2014).Google Scholar
  7. 7.
    V. E. Zakharov, A. I. Dyachenko, and O. A. Vasilyev, “New Method for Nmerical Simulation of a Nonstationary Potential Flow of Incompressible Fluid with a Free Surface,” Europ. J. Mech., B: Fluids 21, 283–291 (2002).CrossRefMATHADSGoogle Scholar
  8. 8.
    P. G. Frik, Turbulence: Methods and Approaches: A Lecture Course (Perm State Technical University, Perm, 1999) [in Russian].Google Scholar
  9. 9.
    R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations (SIAM, Philadelphia, 2007).CrossRefMATHGoogle Scholar
  10. 10.
    L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon Press, Oxford-Elmsford, New York, 1987).MATHGoogle Scholar
  11. 11.
    D. W. Moore, “The Spontaneous Appearance of a Singularity in the Shape of an Evolving Vortex Sheet,” Proc. Roy. Soc. London, Ser. A 365, 105–119 (1979).MathSciNetCrossRefMATHADSGoogle Scholar
  12. 12.
    N. M. Zubarev and E. A. Kuznetsov, “Singularity Formation on a Fluid Interface during the Kelvin-Helmholtz Instability Development,” Zh. Eksp. Tekh. Fiz. 145 (6), 1–11 (2014).Google Scholar
  13. 13.
    D. Pelinovsky, E. Pelinovsky, E. Kartashova, et al., “Universal Power Law for the Energy Spectrum of Breaking Riemann Waves,” Pis’ma Zh. Eksp. Teor. Fiz. 98 (3), 265–269 (2013).Google Scholar

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Electrophysics, Ural BranchRussian Academy of SciencesYekaterinburgRussia

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