Fully nonlinear capillary–gravity wave patterns under the tangential electric field

Tao, Bo; Guo, Dali

doi:10.1016/j.camwa.2013.12.007

Cited by 16 publications

(13 citation statements)

References 12 publications

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“…The kinematic and dynamic boundary conditions at the interface = ( , , ) are given by (see, e.g., [10,22,26]…”

Section: Governing Equationsmentioning

confidence: 99%

“…On the contrary, it can be deduced from the work by Gleeson et al [16], Papageorgiou et al [21], Lin et al [2], and Wang [8] that the normal electric field has a destabilizing effect on the interface. N. M. Zubarev and O. V. Zubareva [10,20] and Tao and Guo [22] considered the electrified gas-fluid or vacuumfluid interface so that they can make the assumption that the permittivity of the fluid was much larger compared to that of gas (the permittivities for pure water and air are 80 and 1, resp.). As a consequence, the actual two-layer problem could be reduced to one layer, and the theoretical and numerical techniques developed for free-surface water wave problems can be generalized to include the electric field.…”

Section: Introductionmentioning

confidence: 99%

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Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Tao

2017

Advances in Mathematical Physics

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We are concerned with gravity-capillary waves propagating on the surface of a three-dimensional electrified liquid sheet under a uniform electric field parallel to the undisturbed free surface. For simplicity, we make an assumption that the permittivity of the fluid is much larger than that of the upper-layer gas; hence, this two-layer problem is reduced to be a one-layer problem. In this paper, we propose model equations in the shallow-water regime based on the analysis of the Dirichlet-Neumann operator. The modified Benney-Luke equation and Kadomtsev-Petviashvili equation will be derived, and the truly three-dimensional fully localized traveling waves, which are known as "lumps" in the literature, are numerically computed in the Benney-Luke equation.

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“…The kinematic and dynamic boundary conditions at the interface = ( , , ) are given by (see, e.g., [10,22,26]…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Tao

2017

Advances in Mathematical Physics

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“…denotes the complex conjugate. Details of the derivation can be found in [14][15][16]. Here we just present the results from the first three orders.…”

Section: Formulationmentioning

confidence: 99%

Dynamics of fully nonlinear capillary–gravity solitary waves under normal electric fields

et al. 2017

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Two-dimensional capillary-gravity waves travelling under the effect of a vertical electric field are considered. The fluid is assumed to be a dielectric of infinite depth. It is bounded above by another fluid which is hydrodynamically passive and perfectly conducting. The problem is solved numerically by time-dependent conformal mapping methods. Fully nonlinear waves are presented, and their stability and dynamics are studied.

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“…The applied interest in studying the liquid surface dynamics in external electric field is related to the possibility of controlling the behavior of liquid surfaces and suppressing hydrodynamic instabilities [7][8][9][10]. The features of the nonlinear evolution of capillary waves at the liquid interfaces in the presence of the horizontal field were analyzed in [11][12][13]. It has been shown in [14][15][16] that, in the case of a strong electric field (the effects of gravitational and capillary forces are negligibly small), nonlinear waves on the surface of a liquid with high dielectric constant can propagate without distortions along (or against) the field direction.…”

Section: Introductionmentioning

confidence: 99%

“…This approach was developed in [19,20] in studying nonlinear waves on the surface of liquids in the absence of an external electric field. The method was used in [13,21,22] for the study of electro-hydrodynamics of liquid dielectrics with free surfaces. At present time, the computational techniques based on the conformal transformations develop intensively; see, for example, [23,24].…”

Section: Introductionmentioning

confidence: 99%

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

Kochurin

Зубарев

2018

IEEE Trans. Dielect. Electr. Insul.

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Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The computational method is based on the time-dependent conformal transformation of the region occupied by the fluid into a half-plane. In the limit of a strong electric field, when the gravitational and capillary forces are negligibly small, there exists an exact analytical solution of the electro-hydrodynamic equations describing propagation without distortions of nonlinear surface waves along (or against) the electric field direction. In the situation where gravity and capillarity are taken into account, the results of numerical simulations indeed show that, for large external field, the waves traveling in a given direction tend to preserve their shape. In the limit of a strong electric field, the interaction of counter-propagating waves leads to the formation of regions, where the electrostatic and dynamic pressures undergo a discontinuity, and the curvature of the surface increases infinitely. The Fourier spectrum of the surface perturbations tends to the power-law distribution (k -2 ). In the case of a finite electric field, the wave interaction results in a radiation of massive cascade of small-scale capillary waves that causes the chaotic behavior of the system. The investigated mechanism of interaction between oppositely-traveling waves can enhance development of the capillary turbulence of the fluid surface.

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Fully nonlinear capillary–gravity wave patterns under the tangential electric field

Cited by 16 publications

References 12 publications

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Dynamics of fully nonlinear capillary–gravity solitary waves under normal electric fields

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

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