21 research outputs found
Exact solutions for equilibrium configurations of charged conducting liquid jets
A wide class of exact solutions is obtained for the problem of finding the
equilibrium configurations of charged jets of a conducting liquid; these
configurations correspond to the finite-amplitude azimuthal deformations of the
surface of a round jet. A critical value of the linear electric charge density
is determined, for which the jet surface becomes self-intersecting, and the jet
splits into two. It exceeds the density value required for the excitation of
the linear azimuthal instability of the round jet. Hence, there exists a range
of linear charge density values, where our solutions may be stable with respect
to small azimuthal perturbations.Comment: 7 pages, 5 figures, to appear in Physical Review
Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence
We report on three-dimensional direct numerical simulation of wave turbulence
on the free surface of a magnetic fluid subjected to an external horizontal
magnetic field. A transition from capillarywave turbulence to anisotropic
magneto-capillary wave turbulence is observed for an increasing field. At high
enough field, wave turbulence becomes highly anisotropic, cascading mainly
perpendicularly to the field direction, in good agreement with the prediction
of a phenomenological model, and with anisotropic Alfv{\'e}n wave turbulence.
Although surface waves on a magnetic fluid are different from Alfv{\'e}n waves
in plasma, a strong analogy is found with similar wave spectrum scalings and
similar magnetic-field dependent dispersionless wave velocities.Comment: in press in Phys. Rev E (Letter). For Supplemental Material, see
http://www.msc.univ-paris-diderot.fr/~falcon/PRE\_Letter22/PRE2022andSuppMat.pd
Wave breaking on the surface of a dielectric liquid in a horizontal electric field
The weakly nonlinear dynamics of the free surface of a dielectric liquid in
an electric field directed tangentially to the unperturbed boundary is
investigated numerically. Within the framework of the strong field model, when
the effects of capillarity and gravity are not taken into account, it is shown
that nonlinear surface waves have a tendency to break. In result of the
collapse of the surface waves, the curvature of the boundary and the gradient
of the local electric field undergo infinite discontinuity on the surface of
the liquid. The angles of the boundary inclination remain small. The
characteristic collapse time of a surface wave traveling in a given direction
is calculated versus the dielectric constant of the liquid. It is shown that
the time of the singularity formation increases infinitely at small and high
values of the dielectric constant. The first case corresponds to the transition
of the system to the neutral stability regime (the jump in electrostatic
pressure at the boundary turns into zero). At high values of the dielectric
constant of the liquid, the collapse time also increases. This effect is
associated with the realization of a special regime of fluid motion, in which
the propagation of nonlinear surface waves of an arbitrary configuration occurs
without distortions. For the liquids with relative permittivity close to five,
the wave breaking time reaches a minimum, i.e., the collapse of the surface
waves for such liquids occurs most intensively.Comment: 7 pages, 5 figure
Numerical Study of Free-Surface Electrohydrodynamic Wave Turbulence
Direct numerical simulation of threedimensional chaotic motion of a
dielectric liquid with a free surface under the action of external horizontal
electric field is carried out. The numerical model takes into account the
effects of surface tension, viscosity, and external isotropic random forcing
acting at large scales. A transition from dispersive capillary wave turbulence
to quasi-isotropic nondispersive EHD surface turbulence with increase of the
external electric field strength is numerically observed for the first time. At
the regime of developed EHD wave turbulence, the total electrical energy is
found to be much greater than the energy of capillary waves, i.e.,
electrohydrodynamic effects play a dominant role. At the same time, anisotropic
effects are detected that lead to the generation of capillary wave packets
traveling perpendicular to the external field direction. Despite the revealed
anisotropy, the calculated spectrum of EHD wave turbulence is in very good
agreement with the analytical spectrum obtained on the basis of dimensional
analysis of weak turbulence spectra.Comment: 7 pages,7 figure
Nonlinear dynamics of the interface of dielectric liquids in a strong electric field: Reduced equations of motion
The evolution of the interface between two ideal dielectric liquids in a
strong vertical electric field is studied. It is found that a particular flow
regime, for which the velocity potential and the electric field potential are
linearly dependent functions, is possible if the ratio of the permittivities of
liquids is inversely proportional to the ratio of their densities. The
corresponding reduced equations for interface motion are derived. In the limit
of small density ratio, these equations coincide with the well-known equations
describing the Laplacian growth.Comment: 10 page