Numerical simulation of the decay interaction of capillary waves

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).

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Numerical simulation of two- and three-dimensional gravity-capillary waves

Journal of Physics Conference Series ◽

10.1088/1742-6596/1163/1/012063 ◽

2019 ◽

Vol 1163 ◽

pp. 012063

Author(s):

A S Dosaev ◽

Yu I Troitskaya

Keyword(s):

Numerical Simulation ◽

Three Dimensional ◽

Capillary Waves ◽

Dimensional Gravity

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Singularities in water waves and the Rayleigh–Taylor problem

Journal of Fluid Mechanics ◽

10.1017/s0022112009992710 ◽

2010 ◽

Vol 651 ◽

pp. 211-239 ◽

Cited By ~ 8

Author(s):

M. A. FONTELOS ◽

F. DE LA HOZ

Keyword(s):

Numerical Simulation ◽

Water Waves ◽

Water Wave ◽

Asymptotic Methods ◽

Logarithmic Spiral ◽

Capillary Waves ◽

Wave Problem ◽

Water Wave Problem ◽

Taylor Problem ◽

Regularizing Effects

We describe, by means of asymptotic methods and direct numerical simulation, the structure of singularities developing at the interface between two perfect, inviscid and irrotational fluids of different densities ρ1 and ρ2 and under the action of gravity. When the lighter fluid is on top of the heavier fluid, one encounters the water-wave problem for fluids of different densities. In the limit when the density of the lighter fluid is zero, one encounters the classical water-wave problem. Analogously, when the heavier fluid is on top of the lighter fluid, one encounters the Rayleigh–Taylor problem for fluids of different densities, with this being the case when one of the densities is zero for the classical Rayleigh–Taylor problem. We will show that both water-wave and Rayleigh–Taylor problems develop singularities of the Moore-type (singularities in the curvature) when both fluid densities are non-zero. For the classical water-wave problem, we propose and provide evidence of the development of a singularity in the form of a logarithmic spiral, and for the classical Rayleigh–Taylor problem no singularities were found. The regularizing effects of surface tension are also discussed, and estimates of the size and wavelength of the capillary waves, bubbles or blobs that are produced are provided.

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