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

Gao, Tao; Milewski, Paul A.; Papageorgiou, Demetrios T.; Vanden‐Broeck, J.‐M.

doi:10.1007/s10665-017-9912-z

Cited by 20 publications

(24 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the simplest case of one soliton N = 1, the solution of the system (8) gives the trajectory of the pole…”

Section: Regular Dynamicsmentioning

confidence: 99%

“…The quantity I = Imp 0 is an integral of motion of the system (8), so that the center p 0 moves in parallel to the real axis. Let |p n − p 0 | |I| for any n, that is, the poles are close to each other on the complex plane.…”

Section: Regular Dynamicsmentioning

confidence: 99%

“…In this section, we study the dynamics of soliton interaction based on the numerical solution of the nonlinear differential Equation (8). For simplicity, we consider the dynamics of interaction of three solitons, that is, N = 3.…”

Section: Chaotic Dynamicsmentioning

confidence: 99%

“…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%

See 3 more Smart Citations

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

View full text Add to dashboard Cite

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.

show abstract

“…For the simplest case of one soliton N = 1, the solution of the system (8) gives the trajectory of the pole…”

Section: Regular Dynamicsmentioning

confidence: 99%

Section: Regular Dynamicsmentioning

confidence: 99%

Section: Chaotic Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

View full text Add to dashboard Cite

show abstract

“…It is noted that there are no studies on time-dependent solutions of the full Euler equations. However, when the fluid is assumed to be a dielectric, and the gas layer a perfect conductor, a time-dependent conformal mapping technique, first pioneered by [19], was employed in [20] to compute the dynamics of solitary waves in deep water. In this work, we generalize the results of [20] to the case of a finite-depth fluid layer and examine the destabilizing effect of the normal electric field.…”

Section: Introductionmentioning

confidence: 99%

Capillary–gravity waves on a dielectric fluid of finite depth under normal electric field

Gao

Doak

Vanden‐Broeck

et al. 2019

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

a b s t r a c tIn this work we consider two-dimensional capillary-gravity waves propagating under the influence of a vertical electric field on a dielectric of finite depth bounded above by a perfectly conducting and hydrodynamically passive fluid. Both linear and weakly nonlinear theories are developed, and long-wave model equations are derived based on the analyticity of the Dirichlet-Neumann operator. Fully nonlinear computations are carried out by using a time-dependent conformal mapping method. Solitary waves are found, and their stability characteristics subject to longitudinal perturbations are studied numerically. The shedding of stable solitary waves is achieved by moving a Gaussian pressure on the free surface with the speed close to a phase speed minimum and removing the pressure after a period of time. The novel result shows that a depression bright solitary wave and an elevation generalized solitary wave co-exist in the solitary-wave excitation.

show abstract

Nonlinear gravity electro-capillary waves in two-fluid systems: solitary and periodic waves and their stability

Broadley

Papageorgiou

2022

J Eng Math

Self Cite

View full text Add to dashboard Cite

Starting from the Euler equations governing the flow of two immiscible incompressible fluids in a horizontal channel, allowing gravity and surface tension, and imposing an electric field across the channel, a nonlinear long-wave analysis is used to derive a $$2\times 2$$ 2 × 2 system of evolution equations describing the interface position and a modified tangential velocity jump across it. Travelling waves of permanent form are shown to exist and are constructed in the periodic case producing wave trains and the infinite case yielding novel gravity electro-capillary solitary waves. Various regimes are analysed including a hydrodynamically passive but electrically active upper layer, pairs of perfect dielectric fluids and a perfectly conducting lower fluid. In all cases, the presence of the field produces both depression and elevation waves travelling at the same speed, for given sets of parameters. The stability of the non-uniform travelling waves is investigated by numerically solving appropriate linearised eigenvalue problems. It is found that depression waves are neutrally stable whereas elevation ones are unstable unless the surface tension is large. Stability or instability is shown to be linked mathematically to the type of local eigenvalues of the nonlinear flux matrix used to obtain travelling and solitary waves; if these are real (hyperbolic flux matrix), the system is stable, and if they are complex (elliptic), the system is unstable. The latter is a manifestation of Kelvin–Helmholtz instability in electrified flows.

show abstract

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

Cited by 20 publications

References 24 publications

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

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

Capillary–gravity waves on a dielectric fluid of finite depth under normal electric field

Nonlinear gravity electro-capillary waves in two-fluid systems: solitary and periodic waves and their stability

Contact Info

Product

Resources

About