Fully nonlinear capillary–gravity solitary waves under a tangential electric field, Part II: Dynamics

Tao, Bo

doi:10.1016/j.camwa.2018.05.019

Cited by 9 publications

(3 citation statements)

References 38 publications

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“…Unsteady simulations were performed based on the time-dependent conformal mapping technique in [15,18] for a special case of capillary-gravity waves on a dielectric fluid of finite and infinite depth respectively covered above by a conducting gas layer. Similar computations have been conducted in [29,43,44] in the presence of horizontal electrical fields. The singularity formation of the capillary-gravity wave due to the effect of normal electric fields was investigated in [55,56].…”

Section: Introductionmentioning

confidence: 68%

Flow structure beneath periodic waves with constant vorticity under normal electric fields

Flamarion

Gao

Ribeiro-Jr³

et al. 2022

Physics of Fluids

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Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. Coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of steady periodic traveling waves with constant vorticity on a dielectric fluid under the effect of normal electric fields. Through the conformal mapping technique combined with pseudo-spectral numerical methods, we develop an approach that allows us to conclude that the flow can have zero, two, or three stagnation points according to variations in the voltage potential. We describe in detail the recirculation zones that emerge together with the stagnation points. In addition, we show that the number of local maxima of the pressure on the bottom boundary is intrinsically connected to the saddle points.

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Section: Introductionmentioning

confidence: 68%

Flow structure beneath periodic waves with constant vorticity under normal electric fields

Flamarion

Gao

Ribeiro-Jr³

et al. 2022

Physics of Fluids

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“…Мы будем рассматривать случай, когда диэлектрическая проницаемость жидкости велика: ε ≫ 1. Как было показано в работах [8], [24], [25] и использовано, например, в [20], [21], в этом случае нормальная компонента электрического поля в жидкости оказывается много меньше тангенциальной компоненты. Это означает, что силовые линии поля внутри жидкости будут направлены по касательной к ее поверхности.…”

Section: исходные уравненияunclassified

Интегрируемая Модель Взаимодействия Встречных Слабонелинейных Волн На Границе Жидкости В Горизонтальном Электрическом Поле

Зубарев¹,

Кочурин²,

Kochurin

2020

TMF

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Рассмотрена нелинейная динамика свободной поверхности диэлектрической жидкости с высокой проницаемостью, находящейся в сильном горизонтальном электрическом поле. В рамках слабонелинейного приближения, когда углы наклона границы считаются малыми и в уравнениях движения учитываются лишь квадратично нелинейные по параметру малости слагаемые, получено компактное модельное уравнение для описания нелинейных волновых процессов в системе. С его использованием аналитически и численно исследовано взаимодействие распространяющихся в противоположных направлениях уединенных поверхностных волн. В частности, продемонстрировано, что встречные волны после взаимодействия восстанавливают свою форму, приобретая при этом некоторый сдвиг фаз. Установлено, что эти свойства модели обусловлены ее интегрируемостью.

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“…It also known that an external electric or magnetic field directed tangentially to the unperturbed interface has a stabilizing effect [3,4]. Thus, the interest to study the interfacial dynamics under the action of external electric field is caused by the possibility of suppressing and controlling hydrodynamic instabilities [5][6][7][8][9][10][11][12][13]. In this work, we investigate the dynamics of interface between dielectric liquids at the regime of stabilized KH instability by tangential electric field.…”

Section: Introductionmentioning

confidence: 99%

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

Kochurin

Зубарев

2021

Fluids

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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.

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Fully nonlinear capillary–gravity solitary waves under a tangential electric field, Part II: Dynamics

Cited by 9 publications

References 38 publications

Flow structure beneath periodic waves with constant vorticity under normal electric fields

Flow structure beneath periodic waves with constant vorticity under normal electric fields

Интегрируемая Модель Взаимодействия Встречных Слабонелинейных Волн На Границе Жидкости В Горизонтальном Электрическом Поле

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

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