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 at initial stages 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 electric field and fluid velocity is accompanied by breaking of surface waves; the inclination angles of the boundary tend to 90∘∘C, and the surface curvature increases without bound.
Citation:
E. A. Kochurin, “Formation of regions with high energy and pressure gradients at the free surface of a liquid dielectric in a tangential electric field”, Prikl. Mekh. Tekh. Fiz., 59:1 (2018), 91–98; J. Appl. Mech. Tech. Phys., 59:1 (2018), 79–85
\Bibitem{Koc18}
\by E.~A.~Kochurin
\paper Formation of regions with high energy and pressure gradients at the free surface of a liquid dielectric in a tangential electric field
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 1
\pages 91--98
\mathnet{http://mi.mathnet.ru/pmtf621}
\crossref{https://doi.org/10.15372/PMTF20180110}
\elib{https://elibrary.ru/item.asp?id=32474743}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 1
\pages 79--85
\crossref{https://doi.org/10.1134/S0021894418010108}
Linking options:
https://www.mathnet.ru/eng/pmtf621
https://www.mathnet.ru/eng/pmtf/v59/i1/p91
This publication is cited in the following 20 articles:
E.A. Kochurin, “Anisotropy of free-surface wave turbulence induced by a horizontal magnetic (electric) field”, Chaos, Solitons & Fractals, 191 (2025), 115828
Evgeny A. Kochurin, Olga V. Zubareva, Mikhail A. Gashkov, “SIMULATION OF CAPILLARY WAVE TURBULENCE ON THE BASIS OF FULLY NONLINEAR PLANE-SYMMETRIC MODEL”, Interfac Phenom Heat Transfer, 12:3 (2024), 17
N. M. Zubarev, E. A. Kochurin, “Influence of an external tangential electric field on the development of capillary turbulence of the free surface of a non-conducting liquid”, J. Appl. Mech. Tech. Phys., 64:3 (2023), 465–471
M. V. Flamarion, E. Kochurin, R. Ribeiro-Jr, “Fully Nonlinear Evolution of Free-Surface Waves with Constant Vorticity under Horizontal Electric Fields”, Mathematics, 11:21 (2023), 4467
E. A. Kochurin, “Simulation of the wave turbulence of a liquid surface using the dynamic conformal transformation method”, JETP Letters, 118:12 (2023), 893–898
Igor A. Dmitriev, Evgeny A. Kochurin, Nikolay M. Zubarev, “Numerical Study of Free-Surface Electro-Hydrodynamic Wave Turbulence”, IEEE Trans. Dielect. Electr. Insul., 30:4 (2023), 1408
Evgeny A. Kochurin, Mikhail A. Gashkov, Nikolay M. Zubarev, 2022 IEEE 21st International Conference on Dielectric Liquids (ICDL), 2022, 1
Oleg V. Gradov, Margaret A. Gradova, Svetlana N. Kholuiskaya, Anatoliy A. Olkhov, “Electron Plasma Charging Effects on the Biocompatible Electrospun Dielectric Fibers”, IEEE Trans. Plasma Sci., 50:1 (2022), 178
Evgeny A. Kochurin, “Numerical simulation of the wave turbulence on the surface of a ferrofluid in a horizontal magnetic field”, Journal of Magnetism and Magnetic Materials, 503 (2020), 166607
M.A. Belyaev, N.M. Zubarev, O.V. Zubareva, “Space-charge-limited current through conical formations on the surface of a liquid with ionic conductivity”, Journal of Electrostatics, 107 (2020), 103478
N. M. Zubarev, E. A. Kochurin, “Integrable model of the interaction of counter-propagating weakly nonlinear waves on the fluid boundary in a horizontal electric field”, Theoret. and Math. Phys., 202:3 (2020), 352–362
E. A. Kochurin, “Wave turbulence of a liquid surface in an external tangential electric field”, JETP Letters, 109:5 (2019), 303–308
E. A. Kochurin, “Formation of weak singularities on the surface of a dielectric fluid in a tangential electric field”, Tech. Phys. Lett., 45:2 (2019), 65–68
K.E. Bobrov, N.M. Zubarev, O.V. Zubareva, 2019 IEEE 20th International Conference on Dielectric Liquids (ICDL), 2019, 1
M.A. Belyaev, N.M. Zubarev, O.V. Zubareva, 2019 IEEE 20th International Conference on Dielectric Liquids (ICDL), 2019, 1
Mikhail A. Gashkov, Gennady A. Mesyats, Nikolay M. Zubarev, Olga V. Zubareva, “Criteria for the Formation of Liquid-Metal Jets in the Cathode Spot of a Vacuum Arc Discharge”, IEEE Trans. Plasma Sci., 47:8 (2019), 3448
Evgeny A. Kochurin, 2019 IEEE 20th International Conference on Dielectric Liquids (ICDL), 2019, 1
N.M. Zubarev, E.A. Kochurin, “NUMERICAL SIMULATION OF WEAK TURBULENCE OF ELECTROCAPILLARY WAVES ON THE SURFACE OF A LIQUID DIELECTRIC”, JOR, 47:1 (2019), 55
E A Kochurin, O V Zubareva, N M Zubarev, “Growth of nonlinear structures on the interface between dielectric liquids in a strong vertical electric field”, J. Phys.: Conf. Ser., 1268:1 (2019), 012026
Mikhail A. Gashkov, Gennady A. Mesyats, Igor V. Uimanov, Nikolay M. Zubarev, “Molten Metal Jets Formation in the Cathode Spot of a Vacuum Arc”, IEEE Trans. Plasma Sci., 47:8 (2019), 3456
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