NUMERICAL SIMULATION OF WEAK TURBULENCE OF ELECTROCAPILLARY WAVES ON THE SURFACE OF A LIQUID DIELECTRIC
Abstract
In the present work, direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field with allowance for viscosity forces has been carried out. In the limit of a strong electric field, when viscous and capillary forces can be neglected, at which the curvature of the boundary increases significantly singular points can form at the boundary of the liquid (Zubarev, Kochurin, 2014, Kochurin, 2018, Kochurin, Zubarev, 2018). In the case of a finite electric field, the interaction of opposing nonlinear electrocapillary waves can lead to the appearance of a direct energy cascade. In the quasi-stationary energy dissipation regime, the probability density functions for the angles of the boundary inclination tend to the normal Gaussian distribution, and the shape of the boundary takes on a complex, chaotic form. The spectrum of the surface disturbances in this mode is described by a power dependence of k–5/2. In terms of energy, the resulting spectrum has the form k–3/2, which coincides with the Iroshnikov-Kraichnan energy spectrum and indicates that the observed wave turbulence of the liquid surface and weak magnetohydrodynamic turbulence of interacting Alfven waves have a related nature.
The work was carried out within the framework of the theme of state assignment 0389-2015-0023 with the support of the Russian Foundation for Basic Research, projects No. 16-38-60002, 19-08-00098, 17-08-00430), the Presidiums of the Russian Academy of Sciences and the Ural Branch of the Russian Academy of Sciences (projects No. 2 and 18-2-2 -15, respectively) and the Council on grants of the President of the Russian Federation (project SP-132.2016.1).
References
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- Kochurin E.A. and Zubarev N.M. Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field. IEEE Transactions on Dielectrics and Electrical Insulation, 2018, Vol. 25, No. 5, pp. 1723–1730.
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Transfer of copyrights occurs on the basis of a license agreement between the Author and Shirshov Institute of Oceanology, RAS
