Advertisement

Fluid Dynamics

, 44:748 | Cite as

Nonlinear waves propagating over a conducting ideal fluid surface in an electric field

  • I. N. Aliev
  • S. O. Yurchenko
Article

Abstract

For wave perturbations of a heavy conducting fluid in an electric field orthogonal to the undisturbed surface evolutionary equations quadratically nonlinear in amplitude are obtained. Equations for the long-wave approximation are derived. A method of deriving the nonlinear and simple-wave equations is proposed. Solutions for solitary waves are considered. It is shown that even a weak electric field significantly affects the form of the soliton solution, which is related with fundamental changes in the spectrum of the linear waves.

Keywords

electrohydrodynamics nonlinear waves soliton Boussinesq equations Korteweg-de Vries equation Schrödinger equation 

References

  1. 1.
    P.N. Antonyuk, “Dispersion Equation for a Plane Capillary-Gravity Wave on a Free Incompressible Viscous Fluid Surface,” Dokl. Akad. Nauk SSSR 286(6), 1324–1328 (1986).MathSciNetGoogle Scholar
  2. 2.
    I.N. Aliev and A.V. Filippov, “Waves Propagating over a Plane Conducting Viscous Fluid Surface in an Electric Field,” Magnitnaya Gidrodinamika, No. 4, 94–98 (1989).Google Scholar
  3. 3.
    A.I. Zhakin, “Nonlinear Waves on the Surface of a Charged Liquid. Instability, Bifurcation, and Nonequilibrium Shapes of the Charged Surface,” Fluid Dynamics 19(3), 422–430 (1984).zbMATHCrossRefGoogle Scholar
  4. 4.
    A.I. Zhakin, “Nonlinear Equilibrium Shapes and Nonlinear Waves on a Ferrofluid (Perfectly Conducting) Surface in a Transverse Magnetic (Electric) Field,” Magnitnaya Gidrodinamika, No. 4, 41–48 (1983).Google Scholar
  5. 5.
    D.F. Belonozhko and A.I. Grigoryev, “Nonlinear Viscous Flows with a Free Surface,” Fluid Dynamics 38(2), 328–335 (2003).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    D.F. Belonozhko and A.I. Grigoryev, “Nonlinear Capillary-Gravity Waves on the Charged Surface of an Ideal Fluid,” Fluid Dynamics 38(6), 916–922 (2003).zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    A.M. Klimov, D.F. Belonozhko, and A.I. Grigoryev, “Nonlinear Periodic Waves on a Charged Free Ideal Fluid Surface,” Zh. Tekhn. Fiz. 74(1), 32–39 (2004).Google Scholar
  8. 8.
    L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 6: Hydrodynamics (Fizmatlit, Moscow, 2003) [in Russian].Google Scholar
  9. 9.
    L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 8: Continuum Electrodynamics (Fizmatlit, Moscow, 2003) [in Russian].Google Scholar
  10. 10.
    V.I. Karpman, Nonlinear Waves in Dispersive Media (Nauka, Moscow, 1973) [in Russian].Google Scholar
  11. 11.
    L.D. Landau and E.M. Lifshits, Theoretical Physics, Vol. 3: Quantum Mechanics (Nonrelativistic Theory) (Fizmatlit, Moscow, 2004) [in Russian].Google Scholar
  12. 12.
    M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, New York, 1989).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • I. N. Aliev
  • S. O. Yurchenko

There are no affiliations available

Personalised recommendations