scholarly journals Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

2021 ◽  
pp. 100224
Author(s):  
Gexing Xu ◽  
Zhi Lin
Keyword(s):  
Electric Field ◽  
Phase Speed ◽  
Capillary Waves ◽  
Minimum Phase ◽  
Bifurcation Mechanism

scholarly journals Universal Stokes’s nanomechanical viscometer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Komal Chaudhary ◽  
Pooja Munjal ◽  
Kamal P. Singh
Keyword(s):  
Electric Field ◽  
Real Time ◽  
Sample Volume ◽  
Capillary Waves ◽  
Small Sample ◽  
Medical Applications ◽  
Rapid Measurement ◽  
Single Lens ◽  
Universal Applicability ◽  
Small Sample Volume

AbstractAlthough, many conventional approaches have been used to measure viscosity of fluids, most methods do not allow non-contact, rapid measurements on small sample volume and have universal applicability to all fluids. Here, we demonstrate a simple yet universal viscometer, as proposed by Stokes more than a century ago, exploiting damping of capillary waves generated electrically and probed optically with sub-nanoscale precision. Using a low electric field local actuation of fluids we generate quasi-monochromatic propagating capillary waves and employ a pair of single-lens based compact interferometers to measure attenuation of capillary waves in real-time. Our setup allows rapid measurement of viscosity of a wide variety of polar, non-polar, transparent, opaque, thin or thick fluids having viscosity values varying over four orders of magnitude from $$10^{0}{-}10^{4}~\text{mPa} \, \text{s}$$ 10 0 - 10 4 mPa s . Furthermore, we discuss two additional damping mechanisms for nanomechanical capillary waves caused by bottom friction and top nano-layer appearing in micro-litre droplets. Such self-stabilized droplets when coupled with precision interferometers form interesting microscopic platform for picomechanical optofluidics for fundamental, industrial and medical applications.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Bo Tao
Keyword(s):  
Electric Field ◽  
Water Waves ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Capillary Waves ◽  
Uniform Electric Field ◽  
Nonlinear Water Waves ◽  
Petviashvili Equation ◽  
Model Equations ◽  
Layer Problem

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.

scholarly journals The generation of gravity–capillary solitary waves by a pressure source moving at a trans-critical speed

2016 ◽  
Vol 810 ◽  
pp. 448-474 ◽  
Author(s):  
Naeem Masnadi ◽  
James H. Duncan
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Model Equation ◽  
Surface Deformation ◽  
Phase Speed ◽  
Capillary Waves ◽  
Deformation Pattern ◽  
Pressure Source ◽  
Exponential Decay Law ◽  
Response State

The unsteady response of a water free surface to a localized pressure source moving at constant speed $U$ in the range $0.95c_{min}\lesssim U\leqslant 1.02c_{min}$, where $c_{min}$ is the minimum phase speed of linear gravity–capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source, and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) and called state III. In the present investigation, cinematic shadowgraph and refraction-based techniques are utilized to measure the temporal evolution of the free-surface deformation pattern downstream of the source as it moves along a towing tank, while numerical simulations of the model equation described by Cho et al. (J. Fluid Mech., vol. 672, 2011, pp. 288–306) are used to extend the experimental results over longer times than are possible in the experiments. From the experiments, it is found that the speed–amplitude characteristics and the shape of the depressions are nearly the same as those of the freely propagating gravity–capillary lumps of inviscid potential theory. The decay rate of the depressions is measured from their height–time characteristics, which are well fitted by an exponential decay law with an order one decay constant. It is found that the shedding period of the depression pairs decreases with increasing source strength and speed. As the source speed approaches $c_{min}$, this period tends to approximately 1 s for all source magnitudes. At the low-speed boundary of state III, a new response with unsteady asymmetric shedding of depressions is found. This response is also predicted by the model equation.

scholarly journals Hydroelastic solitary waves in deep water

2011 ◽  
Vol 679 ◽  
pp. 628-640 ◽  
Author(s):  
PAUL A. MILEWSKI ◽  
J.-M. VANDEN-BROECK ◽  
ZHAN WANG
Keyword(s):  
Solitary Waves ◽  
Small Amplitude ◽  
Moving Load ◽  
Ice Sheets ◽  
Phase Speed ◽  
Elastic Model ◽  
Periodic Waves ◽  
Minimum Phase ◽  
Steady Solutions ◽  
Nonlinear Elastic

The problem of waves propagating on the surface of a two-dimensional ideal fluid of infinite depth bounded above by an elastic sheet is studied with asymptotic and numerical methods. We use a nonlinear elastic model that has been used to describe the dynamics of ice sheets. Particular attention is paid to forced and unforced dynamics of waves having near-minimum phase speed. For the unforced problem, we find that wavepacket solitary waves bifurcate from nonlinear periodic waves of minimum speed. When the problem is forced by a moving load, we find that, for small-amplitude forcing, steady responses are possible at all subcritical speeds, but for larger loads there is a transcritical range of forcing speeds for which there are no steady solutions. In unsteady computations, we find that if the problem is forced at a speed in this range, very large unsteady responses are obtained, and that when the forcing is released, a solitary wave is generated. These solitary waves appear stable, and can coexist within a sea of small-amplitude waves.

scholarly journals Resonantly forced gravity–capillary lumps on deep water. Part 1. Experiments

2011 ◽  
Vol 672 ◽  
pp. 268-287 ◽  
Author(s):  
JAMES D. DIORIO ◽  
YEUNWOO CHO ◽  
JAMES H. DUNCAN ◽  
T. R. AKYLAS
Keyword(s):  
Surface Pressure ◽  
Deep Water ◽  
Measurement Techniques ◽  
Phase Speed ◽  
Wave Pattern ◽  
Capillary Waves ◽  
Pressure Amplitude ◽  
Pressure Source ◽  
Nonlinear Features ◽  
Pressure Magnitude

The wave pattern generated by a pressure source moving over the free surface of deep water at speeds, U, below the minimum phase speed for linear gravity–capillary waves, cmin, was investigated experimentally using a combination of photographic measurement techniques. In similar experiments, using a single pressure amplitude, Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) pointed out that the resulting surface response pattern exhibits remarkable nonlinear features as U approaches cmin, and three distinct response states were identified. Here, we present a set of measurements for four surface-pressure amplitudes and provide a detailed quantitative examination of the various behaviours. At low speeds, the pattern resembles the stationary state (U = 0), essentially a circular dimple located directly under the pressure source (called a state I response). At a critical speed, but still below cmin, there is an abrupt transition to a wave-like state (state II) that features a marked increase in the response amplitude and the formation of a localized solitary depression downstream of the pressure source. This solitary depression is steady, elongated in the cross-stream relative to the streamwise direction, and resembles freely propagating gravity–capillary ‘lump’ solutions of potential flow theory on deep water. Detailed measurements of the shape of this depression are presented and compared with computed lump profiles from the literature. The amplitude of the solitary depression decreases with increasing U (another known feature of lumps) and is independent of the surface pressure magnitude. The speed at which the transition from states I to II occurs decreases with increasing surface pressure. For speeds very close to the transition point, time-dependent oscillations are observed and their dependence on speed and pressure magnitude are reported. As the speed approaches cmin, a second transition is observed. Here, the steady solitary depression gives way to an unsteady state (state III), characterized by periodic shedding of lump-like disturbances from the tails of a V-shaped pattern.

scholarly journals Fine Scale Dynamics of Fragmented Aurora-Like Emission

2021 ◽  
Author(s):  
Daniel K. Whiter ◽  
Hanna Dahlgren ◽  
Betty S. Lanchester ◽  
Joshua Dreyer ◽  
Noora Partamies ◽  
...  
Keyword(s):  
Electric Field ◽  
Strong Electric Field ◽  
Phase Speed ◽  
Optical Observations ◽  
Internal Dynamics ◽  
Group Speed ◽  
Speed Group ◽  
E Region ◽  
Energetic Particle Precipitation ◽  
Normal Sense

Abstract. Fragmented Aurora-like Emissions (FAEs) are small (few km) optical structures which have been observed close to the poleward boundary of the aurora from the high-latitude location of Svalbard (magnetic latitude 75.3 ° N). The FAEs are only visible in certain emissions and their shape has no magnetic-field aligned component, suggesting that they are not caused by energetic particle precipitation and are therefore not aurora in the normal sense of the word. The FAEs sometimes form wave-like structures parallel to an auroral arc, with regular spacing between each FAE. They drift at a constant speed and exhibit internal dynamics moving at a faster speed than the envelope structure. The formation mechanism of FAEs is currently unknown. We present an analysis of high-resolution optical observations of FAEs made during two separate events. Based on their appearance and dynamics we make the assumption that the FAEs are a signature of a dispersive wave in the lower E-region ionosphere, co-located with enhanced electron and ion temperatures detected by incoherent scatter radar. Their drift speed (group speed) is found to be 580–700 m s−1 and the speed of their internal dynamics (phase speed) is found to be 2200–2500 m s−1, both for an assumed altitude of 100 km. The speeds are similar for both events which are observed during different auroral conditions. We consider two possible waves which could produce the FAEs, electrostatic ion cyclotron waves and Farley-Buneman waves, and find that the observations could be consistent with either wave under certain assumptions. In the case of EIC waves the FAEs must be located at an altitude above about 140 km, and our measured speeds scaled accordingly. In the case of Farley-Buneman waves a very strong electric field of about 365 mV m−1 is required to produce the observed speeds of the FAEs; such a strong electric field may be a requirement for FAEs to occur.

scholarly journals Fine-scale dynamics of fragmented aurora-like emissions

2021 ◽  
Vol 39 (6) ◽  
pp. 975-989
Author(s):  
Daniel K. Whiter ◽  
Hanna Sundberg ◽  
Betty S. Lanchester ◽  
Joshua Dreyer ◽  
Noora Partamies ◽  
...  
Keyword(s):  
Electric Field ◽  
Strong Electric Field ◽  
Phase Speed ◽  
Optical Observations ◽  
Internal Dynamics ◽  
Group Speed ◽  
Speed Group ◽  
E Region ◽  
Energetic Particle Precipitation ◽  
Normal Sense

Abstract. Fragmented aurora-like emissions (FAEs) are small (few kilometres) optical structures which have been observed close to the poleward boundary of the aurora from the high-latitude location of Svalbard (magnetic latitude 75.3 ∘N). The FAEs are only visible in certain emissions, and their shape has no magnetic-field-aligned component, suggesting that they are not caused by energetic particle precipitation and are, therefore, not aurora in the normal sense of the word. The FAEs sometimes form wave-like structures parallel to an auroral arc, with regular spacing between each FAE. They drift at a constant speed and exhibit internal dynamics moving at a faster speed than the envelope structure. The formation mechanism of FAEs is currently unknown. We present an analysis of high-resolution optical observations of FAEs made during two separate events. Based on their appearance and dynamics, we make the assumption that the FAEs are a signature of a dispersive wave in the lower E-region ionosphere, co-located with enhanced electron and ion temperatures detected by incoherent scatter radar. Their drift speed (group speed) is found to be 580–700 m s−1, and the speed of their internal dynamics (phase speed) is found to be 2200–2500 m s−1, both for an assumed altitude of 100 km. The speeds are similar for both events which are observed during different auroral conditions. We consider two possible waves which could produce the FAEs, i.e. electrostatic ion cyclotron waves (EIC) and Farley–Buneman waves, and find that the observations could be consistent with either wave under certain assumptions. In the case of EIC waves, the FAEs must be located at an altitude above about 140 km, and our measured speeds scaled accordingly. In the case of Farley–Buneman waves a very strong electric field of about 365 mV m−1 is required to produce the observed speeds of the FAEs; such a strong electric field may be a requirement for FAEs to occur.

scholarly journals NUMERICAL SIMULATION OF WEAK TURBULENCE OF ELECTROCAPILLARY WAVES ON THE SURFACE OF A LIQUID DIELECTRIC

2019 ◽  
Vol 47 (1) ◽  
pp. 55-57
Author(s):  
N.M. Zubarev ◽  
E.A. Kochurin
Keyword(s):  
Numerical Simulation ◽  
Electric Field ◽  
Strong Electric Field ◽  
Basic Research ◽  
Capillary Waves ◽  
Liquid Dielectric ◽  
Russian Academy Of Sciences ◽  
Direct Energy ◽  
The Russian Federation ◽  
Academy Of Sciences

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).

Particle trajectories in nonlinear capillary waves

1984 ◽  
Vol 143 ◽  
pp. 243-252 ◽  
Author(s):  
S. J. Hogan
Keyword(s):  
Drift Velocity ◽  
Phase Speed ◽  
Analytic Form ◽  
Capillary Waves ◽  
Particle Trajectories

The particle trajectories of nonlinear capillary waves are derived. The properties of the surface and subsurface particles are presented in exact analytic form, up to and including the highest wave. It is found that the orbits of the steeper waves are neither circular nor closed. For the highest wave, a particle moves through a distance [X] equal to 7.99556 λ in one orbit, where λ is the wavelength. It moves with an average horizontal drift velocity U equal to 0.88883c, where c is the phase speed of the wave. In addition, the subsurface particles (at depths nearly three-quarters that of the wavelength) move at speeds up to one-tenth that of surface particles.

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