ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 79–85.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
FORMATION OF REGIONS WITH HIGH ENERGY
AND PRESSURE GRADIENTS AT THE FREE SURFACE
OF LIQUID DIELECTRIC IN A TANGENTIAL ELECTRIC FIELD
E. A. Kochurin
Abstract: 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.
Keywords: free surface, nonlinear waves, electric ﬁeld, electrohydrodynamics, wave breaking,
It is known that an external electric ﬁeld directed tangentially to the undisturbed ﬂuid surface exerts a
stabilizing eﬀect on the ﬂuid surface . The possibility of suppressing hydrodynamic instabilities such as Rayleigh–
Taylor or Kelvin–Helmholtz instabilities was analyzed, e.g., in [2, 3]. It has been found  that in the absence of
destabilizing factors, nonlinear waves of arbitrary shape can propagate without distortions along the surface of a
nonconducting ﬂuid with a high dielectric constant in the direction of the applied strong tangential electric ﬁeld and
in the opposite direction. In , this result was extended to weakly nonlinear waves at the interface of two immiscible
ﬂuids. It has been found  that the interaction of localized nonlinear waves on a free ﬂuid boundary is elastic (the
energy and momentum of each wave are conserved), and in the case of solitary waves, it is relatively weak.
In this paper, we consider the interaction of periodic counter-propagating waves of signiﬁcant amplitude.
The dynamics of a nonconducting ﬂuid is modeled using the method based on conformal transformation of the
ﬂuid-ﬁlled region into a half-plane and proposed in  to describe the dynamics of nonlinear waves on a ﬂuid surface
under gravity. It has been shown that in the initial stage of interaction of periodic waves, the so-called direct energy
cascade occurs , which leads to excitation of short-wavelength harmonics, i.e., there is energy transfer to small
scales. During excitation of high-frequency harmonics, regions with high energy densities and electric-ﬁeld gradients
are formed at the ﬂuid boundary.
Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016 Russia;
email@example.com. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 91–98,
January–February, 2018. Original article submitted October 31, 2016; revision submitted December 7, 2016.
2018 by Pleiades Publishing, Ltd.