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

Chaotic Dynamics of the Interface between Dielectric Liquids at the Regime of Stabilized Kelvin-Helmholtz Instability by a Tangential Electric Field

The nonlinear dynamics of the interface between two immiscible dielectric liquids at the regime of suppressed Kelvin-Helmholtz instability by external horizontal electric field is studied theoretically. The initial equations of the fluids motion are reduced to a single weakly nonlinear integro-differential equation that describes the interaction of solitary waves (rational solitons) propagating along the interface. The dynamics of two interacting solitons is regular and integrable; they can combine into a stable wave packet (breather). It is shown that the interaction of three solitons becomes complex and, for a wide rang of initial conditions, chaotic. The numerically obtained Poincaré sections demonstrate the destruction of toroidal trajectories in the phase space during the transition of the system to a chaotic regime of fluid motion. Such a behaviour is consistent with the Kolmogorov-Arnold-Moser theory describing quasi-periodic chaotic motion in Hamiltonian systems. At the developed chaotic state, the system fast loses the information on its initial state; the corresponding estimate for Lyapunov exponent is obtained. From the physical point of view, the chaotic behavior of the system is related with structural instability of the soliton triplet. The triplet can decay into a solitary wave and stable breather consisting of two interacting solitons