scholarly journals Spatiotemporal measurement of surfactant distribution on gravity–capillary waves

2015 ◽  
Vol 777 ◽  
pp. 523-543 ◽  
Author(s):  
Stephen L. Strickland ◽  
Michael Shearer ◽  
Karen E. Daniels
Keyword(s):  
Surface Waves ◽  
Travelling Waves ◽  
Leading Edge ◽  
Capillary Waves ◽  
Density Field ◽  
Faraday Waves ◽  
Non Invasive ◽  
Temporal Phase ◽  
Insoluble Surfactant ◽  
Biogenic Slicks

Materials adsorbed onto the surface of a fluid – for instance, crude oil, biogenic slicks or industrial/medical surfactants – will move in response to surface waves. Owing to the difficulty of non-invasive measurement of the spatial distribution of a molecular monolayer, little is known about the dynamics that couple the surface waves and the evolving density field. Here, we report measurements of the spatiotemporal dynamics of the density field of an insoluble surfactant driven by gravity–capillary waves in a shallow cylindrical container. Standing Faraday waves and travelling waves generated by the meniscus are superimposed to create a non-trivial surfactant density field. We measure both the height field of the surface using moiré imaging, and the density field of the surfactant via the fluorescence of NBD-tagged phosphatidylcholine, a lipid. Through phase averaging stroboscopically acquired images of the density field, we determine that the surfactant accumulates on the leading edge of the travelling meniscus waves and in the troughs of the standing Faraday waves. We fit the spatiotemporal variations in the two fields using an ansatz consisting of a superposition of Bessel functions, and report measurements of the wavenumbers and energy damping factors associated with the meniscus and Faraday waves, as well as the spatial and temporal phase shifts between them. While these measurements are largely consistent for both types of waves and both fields, it is notable that the damping factors for height and surfactant in the meniscus waves do not agree. This raises the possibility that there is a contribution from longitudinal waves in addition to the gravity–capillary waves.

Symmetry-breaking bifurcations in resonant surface waves

1989 ◽  
Vol 199 ◽  
pp. 495-518 ◽  
Author(s):  
Z. C. Feng ◽  
P. R. Sethna
Keyword(s):  
Normal Form ◽  
Symmetry Breaking ◽  
Surface Waves ◽  
Bifurcation Analysis ◽  
Internal Resonance ◽  
Travelling Waves ◽  
Chaotic Behaviour ◽  
Derived Set ◽  
Parameter Values ◽  
Theoretical Results

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

Application Of Elastic Layers To Register Pressure Field On The Model Surface In Supersonic Flow

2016 ◽  
Vol 11 (1) ◽  
pp. 23-33
Author(s):  
Maxim Golubev ◽  
Andrey Shmakov
Keyword(s):  
Surface Waves ◽  
High Frequency ◽  
High Speed ◽  
Pressure Pulsation ◽  
Pressure Field ◽  
Leading Edge ◽  
Supersonic Wind Tunnel ◽  
Register Pressure ◽  
Elastic Layers ◽  
Sharp Leading Edge

The work presents the results of application of panoramic interferential technique which is based on elastic layers (sensors) usage to obtain pressure distribution on the flat plate having sharp leading edge. Experiments were done in supersonic wind tunnel at Mach number M = 4. Sensitivity and response time are shown to be enough to register pressure pulsation against standing and traveling sensor surface waves. Applying high-frequency image acquiring is demonstrated to make possible to distinguish at visualization images high-speed disturbances propagating in the boundary layer from low-speed surface waves

Flow Behavior of a Centrifugal Compressor With Vaneless Diffuser at Design and Off Design Conditions

2012 ◽  
Author(s):  
Chuang Gao ◽  
Weiguang Huang ◽  
Haiqing Liu ◽  
Hongwu Zhang ◽  
Jundang Shi
Keyword(s):  
Centrifugal Compressor ◽  
Flow Behavior ◽  
Travelling Waves ◽  
Leading Edge ◽  
Pressure Oscillation ◽  
Rotating Stall ◽  
Vaneless Diffuser ◽  
Unstable Flow ◽  
Flow Recirculation ◽  
Static Performance

This paper concerns with the numerical and experimental aspects of both steady and unsteady flow behavior in a centrifugal compressor with vaneless diffuser and downstream collector. Specifically, the appearance of flow instabilities i.e., rotating stall and surge is investigated in great detail. As the first step, the static performance of both stage and component was analyzed and possible root cause of system surge was put forward based on the classic stability theory. Then the unsteady pressure data was utilized to find rotating stall and surge in frequency domain which could be classified as mild surge and deep surge. With the circumferentially installed transducers at impeller inlet, backward travelling waves during stall ramp could be observed. The modes of stall waves could be clearly identified which is caused by impeller leading edge flow recirculation at Mu = 0.96. However, for the unstable flow at Mu = 1.08, the system instability seems to be caused by reversal flow in vaneless diffuser where the pressure oscillation was strongest. Thus steady numerical simulation were performed and validated with the experimental performance data. With the help of numerical analysis, the conjectures are proved.

scholarly journals Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited

2015 ◽  
Vol 777 ◽  
Author(s):  
Jean Rajchenbach ◽  
Didier Clamond
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Significant Role ◽  
Current Literature ◽  
Theoretical Description ◽  
Long Waves ◽  
Faraday Waves ◽  
Wavenumber Selection

In the current literature, the dispersion relation of parametrically forced surface waves is often identified with that of free unforced waves. We revisit here the theoretical description of Faraday waves, showing that forcing and dissipation play a significant role in the dispersion relation, rendering it bi-valued. We then determine the instability thresholds and the wavenumber selection in cases of both short and long waves. We show that the bifurcation can be either supercritical or subcritical, depending on the depth.

Theoretical aspects of gravity–capillary waves in non-rectangular channels

1995 ◽  
Vol 290 ◽  
pp. 377-404 ◽  
Author(s):  
Mark D. Groves
Keyword(s):  
Travelling Waves ◽  
Normal Modes ◽  
Nonlinear Problems ◽  
Travelling Wave ◽  
Capillary Waves ◽  
Theoretical Research ◽  
Existence Theory ◽  
Water Wave Problem ◽  
Qualitative Comparison ◽  
Free Edges

This article reports the results of theoretical research concerning linear waves propagating on the surface of water in a uniform horizontal channel of arbitrary crosssection. Three different versions of the problem are considered. The first is the hydrodynamic problem when surface tension is neglected. The second and third include capillary effects, necessitating the use of edge conditions at the points of contact of the free edges and the channel walls. Two sets of edge constraints are used: pinned edges, where the lines of contact are fixed, and free edges, where the surface meets locally vertical walls orthogonally. These choices are physically realistic and have certain advantages for mathematical analysis.The hydrodynamic problems are shown to have a Hamiltonian structure in which the non-local operators inherent in the water-wave problem are explicitly exhibited. The existence, properties and applications of normal-mode solutions are discussed, and a qualitative comparison of those obtained for each problem is given. Explicit and numerical calculations of the dispersion relations for the normal modes are also carried out. A long-wave theory based upon a decomposition of the hydrodynamic problems in Fourier-transform space is developed. Finally a bifurcation theory for linear travelling waves is discussed, a potential application of which is the construction of an existence theory for periodic travelling-wave solutions of the corresponding nonlinear problems.

scholarly journals Gamma Entrainment Improves Synchronization Deficits in Dementia Patients

2021 ◽  
Author(s):  
Mojtaba Lahijanian ◽  
Hamid Aghajan ◽  
Zahra Vahabi ◽  
Arshia Afzal
Keyword(s):  
Oscillatory Activity ◽  
Therapeutic Effects ◽  
Phase Coupling ◽  
Non Invasive ◽  
Temporal Phase ◽  
Dementia Patients ◽  
Frequency Coupling ◽  
Phase Amplitude ◽  
Cross Frequency Coupling

AbstractNon-invasive gamma entrainment has shown promising results in alleviating cognitive symptoms of Alzheimer’s disease in mice and humans. In this study, we examine improvements in the synchronization characteristics of the brain’s oscillations induced by 40Hz auditory stimulation based on electroencephalography data recorded from a group of dementia patients. We observed that when the quality of entrainment surpasses a certain level, several indicators of brain synchronization significantly improve. Specifically, the entrained oscillatory activity maintains temporal phase stability in the frontal, parietal, and occipital regions, and persistent spatial phase coupling between them. In addition, notable theta-gamma phase-amplitude coupling is observed in these areas. Interestingly, a high theta power at rest predicts the quality of entrainment. We identify differentiating attributes of temporal/spatial synchronization and cross-frequency coupling in the data of two groups with entrained and non-entrained responses which point to enhanced network synchronization caused by entrainment and can explain its potential therapeutic effects.

Gravity–capillary jet-like surface waves generated by an underwater bubble

2019 ◽  
Vol 866 ◽  
pp. 841-864 ◽  
Author(s):  
Youn J. Kang ◽  
Yeunwoo Cho
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Pattern ◽  
Capillary Waves ◽  
Maximum Height ◽  
Gravitational Acceleration ◽  
Poisson Problem ◽  
Conservation Of Momentum ◽  
Proportional Relationship ◽  
The Difference

Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble ($d$: 0.28–7 mm) below the free surface and the maximum radius of the bubble ($R_{m}$: 1.5–3.6 mm). When $d/R_{m}>1.3$, the surface wave shows a simple smooth hump (case 1). When $0.82<d/R_{m}<1.3$, a single droplet or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the jet-like surface wave (case 2). Finally, when $d/R_{m}<0.82$, a series of squirting and jetting phenomena are observed at the top of the jet-like surface wave (case 3). For case 1, a proportional relationship is found between $\unicode[STIX]{x1D70C}gh/\unicode[STIX]{x0394}p$ and $(d/R_{m})^{-4.4}$, where $\unicode[STIX]{x1D70C}$ is the density of the fluid, $g$ is the gravitational acceleration and $\unicode[STIX]{x0394}p$ is the difference between the reference atmospheric pressure and the vapour pressure inside a bubble. This proportional relationship is explained semi-analytically using a scaling argument and conservation of momentum and energy, with the help of the Kelvin impulse theory. In addition, we solve the relevant axisymmetric Cauchy–Poisson problem where the initial condition is a jet-like surface wave near its maximum height. By comparing the analytical wave solution with the observed surface wave pattern, it is found that the resultant surface waves are indeed gravity–capillary waves where both the gravity and the surface tension are equally important.

Gentle spilling breakers: crest profile evolution

1999 ◽  
Vol 379 ◽  
pp. 191-222 ◽  
Author(s):  
JAMES H. DUNCAN ◽  
HAIBING QIAO ◽  
VASANTH PHILOMIN ◽  
ALEXANDRA WENZ
Keyword(s):  
Surface Profile ◽  
Leading Edge ◽  
Capillary Waves ◽  
Wave Crest ◽  
Fixed Position ◽  
Left Behind ◽  
The Face ◽  
Mean Water Level ◽  
The Mean ◽  
Spilling Breakers

The surface profile histories of gentle spilling breakers generated mechanically with a dispersive focusing technique are studied experimentally. Froude-scaled generation conditions are used to produce waves with three average frequencies: f0=1.42, 1.26, and 1.15 Hz. At each frequency, the strength of the breaker is varied by varying the overall amplitude of the wavemaker motion. It is found that in all cases the beginning of the breaking process is marked by the formation of a bulge in the profile at the crest on the forward face of the wave. The leading edge of this bulge is called the toe. As the breaking process continues, the bulge becomes more pronounced while the toe remains in nearly a fixed position relative to the crest. Capillary waves form ahead of the toe. At a time of about 0.1/f0 after the bulge first becomes visible, the toe begins to move down the face of the wave and very quickly accelerates to a constant velocity which scales with the wave crest speed. During this phase of the breaker evolution, the surface profile between the toe and the crest develops ripples which eventually are left behind the wave crest. It is found that the height of the toe above the mean water level scales with the nominal wavelength λ0=g/(2πf20) of the breaker, while the size and shape of the bulge and the length of the capillary waves ahead of the toe are independent of f0.

scholarly journals Transversally periodic solitary gravity–capillary waves

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130537 ◽  
Author(s):  
Paul A. Milewski ◽  
Zhan Wang
Keyword(s):  
Solitary Waves ◽  
Water Waves ◽  
Travelling Waves ◽  
Plane Waves ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Propagation Direction ◽  
The Stability ◽  
Dirichlet To Neumann Operator ◽  
The Waves

When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.

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