Experimental study of wave propagation on liquid/air surfaces under perpendicular electric field

Koulova, Dantchi; Romat, H.; Louste, Christophe

doi:10.1109/tdei.2018.007389

Cited by 13 publications

(8 citation statements)

References 21 publications

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“…После взаимодействия в этом приближении они сохраняют и форму, и фазу. Отметим, что (11) является также решением уравнения (5) (см. [8]).…”

Section: аналитическое исследование взаимодействия слабонелинейных волнunclassified

“…Это связано с тем, что уравнения (4) и (5) идентичны в квадратичном приближении. Как следствие, решение (11) одновременно (с соответствующей точностью) обеспечивает выполнение законов сохранения (6) и ( 7) уравнений (4) и (5). Ищем следующее, кубически-нелинейное приближение.…”

Section: аналитическое исследование взаимодействия слабонелинейных волнunclassified

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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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Section: аналитическое исследование взаимодействия слабонелинейных волнunclassified

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

Зубарев¹,

Кочурин²,

Kochurin

2020

TMF

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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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“…For this reason, in this work we will use the previously obtained results for non-conducting liquids in an electric field. The dynamics of coherent structures (solitons or collapses) on the surface of liquids in a magnetic (electric) field has been very well studied (see, for example, [Koulova et al(2018)Koulova, Romat, and Louste, Bourdin et al(2010)Bourdin, Bacri, andFalcon, Tao(2018), Zubarev(2002), Vanden-Broeck et al(2019)Vanden-Broeck, Gao, Doak, and Wang]). At the same time, the turbulence of surface waves in an external electromagnetic field was not theoretically investigated (except of our recent work [Kochurin(2019)]).…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the wave turbulence on the surface of a ferrofluid in a horizontal magnetic field

Kochurin

2020

Preprint

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The turbulence of capillary waves on the surface of a ferrofluid with a high permeability in a horizontal magnetic field is considered in the framework of a one-dimensional weakly nonlinear model. In the limit of a strong magnetic field, the surface waves under study can propagate without distortions along or against the direction of external field, i.e., similar to Alfvén waves in a perfectly conducting fluid. The interaction of counter-propagating nonlinear waves leads to the development of wave turbulence on the surface of the liquid.The computational data show that the spectrum of turbulence is divided into two parts: a low-frequency dispersionless region, where the magnetic forces dominate and a high-frequency dispersive one, in which the influence of capillary forces becomes significant. In the first region, the spectrum of the surface elevation has the same exponent in k and ω domains and its value is close to −3.5, what is in a good agreement with the estimation obtained from the dimensional analysis of the weak turbulence spectra. At the high frequencies, the computed spatial spectrum of the surface waves is close to k −5/2 which corresponds to ω −5/3 in terms of the frequency. This spectrum does not coincide with the Zakharov-Filonenko spectrum obtained for pure capillary waves. A possible explanation of this fact is in the influence of coherent structures (like shock waves) usually arising in media with weak dispersion.

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Experimental study of wave propagation on liquid/air surfaces under perpendicular electric field

Cited by 13 publications

References 21 publications

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

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

Numerical simulation of the wave turbulence on the surface of a ferrofluid in a horizontal magnetic field

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