scholarly journals Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Raffaele Colombi ◽  
Niclas Rohde ◽  
Michael Schlüter ◽  
Alexandra Von Kameke
Keyword(s):  
Three Dimensional ◽  
Vertical Direction ◽  
Velocity Fields ◽  
Surface Flow ◽  
Energy Cascade ◽  
Surface Velocity ◽  
Faraday Waves ◽  
Piv Measurements ◽  
Fluid Surface ◽  
Inverse Energy Cascade

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at  the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

scholarly journals Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

2020 ◽  
Vol 62 (1) ◽  
Author(s):  
Raffaele Colombi ◽  
Michael Schlüter ◽  
Alexandra von Kameke
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Velocity Fields ◽  
Surface Flow ◽  
Two Dimensional ◽  
Faraday Waves ◽  
2D Turbulence

Abstract Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow. Graphic abstract

scholarly journals Three-dimensional hydrodynamics numerical of wind-driven circulations in Danjiangkou Reservoir

2018 ◽  
Vol 246 ◽  
pp. 02021
Author(s):  
Jie Zhu ◽  
Jin Quan ◽  
Xiaohui Lei ◽  
Xia Yue ◽  
Yang Duan
Keyword(s):  
Wind Speed ◽  
Flow Field ◽  
Potential Flow ◽  
Flow Direction ◽  
Three Dimensional ◽  
Surface Flow ◽  
Surface Velocity ◽  
Wind Condition ◽  
Reservoir Area ◽  
Danjiangkou Reservoir

This paper focuses on the analysis of the flow field of Danjiangkou Reservoir under the action of wind stress. Based on the analysis of the annual wind field data of Danjiangkou Reservoir, the three-dimensional hydrodynamic model of Danjiangkou Reservoir was established. The distribution of water flow field in the reservoir area under five different wind directions and two different wind speeds was studied. The simulation results were compared with the flow field without wind. The results show that when the wind speed in the reservoir area is 3.3m/s, the surface velocity and flow direction change less under the same wind conditions as the potential flow direction. Under the wind condition opposite to the potential flow direction, the reservoir area is locally generated. The small circulation and surface flow are more disordered; when the wind speed reaches 10.0m/s, under the same wind condition as the potential flow direction, the surface velocity of the reservoir area increases significantly. Under the wind condition opposite to the direction of the potential flow, a stable counterclockwise circulation is generated, and the wind direction dominates the surface layer. seriously affecting the flow field distribution in the reservoir area. The research results in this paper can provide support for the reservoir in the formulation of emergency water pollution emergency strategy and the formulation of real-time scheduling plan.

scholarly journals TURBULENCE DRIVEN BY FARADAY SURFACE WAVES

2014 ◽  
Vol 34 ◽  
pp. 1460379 ◽  
Author(s):  
MICHAEL SHATS ◽  
NICOLAS FRANCOIS ◽  
HUA XIA ◽  
HORST PUNZMANN
Keyword(s):  
Turbulent Flows ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Spectral Energy ◽  
Vertical Acceleration ◽  
Faraday Waves ◽  
Frequency Spectra ◽  
Inverse Energy Cascade ◽  
Lagrangian Velocity ◽  
Measuring Frequency

We report experimental results which show that the particle motion on the surface perturbed by Faraday waves is similar to the fluid motion in 2D turbulence. It supports the inverse energy cascade or the spectral energy transfer from smaller to larger scales. The vertical acceleration ranges from the Faraday instability threshold up to the droplet nucleation threshold where the ripples are a couple of millimeters high. Such a configuration rules out any 2D assumption on the fluid motion. The motion of floaters on the surface of the Faraday waves is essentially three dimensional but its horizontal component shows unexpected analogy with two-dimensional turbulence. The presence of the inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity and confirmed by computing the third moment of the horizontal Eulerian velocity fluctuations. This is a robust phenomenon observed in deep water in a broad range of flow energies and wavelengths. The emergence of such a phenomenology in Faraday waves broadens the applicability of features common to 2D turbulent flows to the context of surface wave phenomena which is prevalent in many systems.

Diffusion of swimming model micro-organisms in a semi-dilute suspension

2007 ◽  
Vol 588 ◽  
pp. 437-462 ◽  
Author(s):  
TAKUJI ISHIKAWA ◽  
T. J. PEDLEY
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Reynolds Numbers ◽  
Surface Velocity ◽  
Biased Random Walk ◽  
Long Time ◽  
Upward Velocity ◽  
Micro Organisms ◽  
Diffusive Behaviour

The diffusive behaviour of swimming micro-organisms should be clarified in order to obtain a better continuum model for cell suspensions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 or 27 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. In the case of (non-bottom-heavy) squirmers, both the translational and the orientational spreading of squirmers is correctly described as a diffusive process over a sufficiently long time scale, even though all the movements of the squirmers were deterministically calculated. Scaling of the results on the assumption that the squirmer trajectories are unbiased random walks is shown to capture some but not all of the main features of the results. In the case of (bottom-heavy) squirmers, the diffusive behaviour in squirmers' orientations can be described by a biased random walk model, but only when the effect of hydrodynamic interaction dominates that of the bottom-heaviness. The spreading of bottom-heavy squirmers in the horizontal directions show diffusive behaviour, and that in the vertical direction also does when the average upward velocity is subtracted. The rotational diffusivity in this case, at a volume fractionc=0.1, is shown to be at least as large as that previously measured in very dilute populations of swimming algal cells (Chlamydomonas nivalis).

scholarly journals Application of an Entropic Method Coupled with STIV for Discharge Measurement in Actual Rivers

2021 ◽  
Vol 945 (1) ◽  
pp. 012036
Author(s):  
Yoshiro Omori ◽  
Ichiro Fujita ◽  
Ken Watanabe
Keyword(s):  
Velocity Distribution ◽  
Flow Velocity ◽  
River Flow ◽  
Measurement Techniques ◽  
Vertical Direction ◽  
Acoustic Doppler Current Profiler ◽  
Surface Flow ◽  
Surface Velocity ◽  
Cross Sectional ◽  
Current Profiler

Abstract In recent years, due to the frequent occurrence of floods that exceed the facility maintenance level due to climate change, non-contact flood flow measurement techniques have been paid attention and actually some measurements have been conducted by applying them instead of the conventional float method. The space-time image velocimetry (STIV) which can measure the surface flow velocity distribution from video images is one of such techniques. In order to calculate the river flow from the surface velocity distribution, it is necessary to determine an appropriate surface velocity coefficient, which is the ratio of the average depth velocity to the surface velocity. However, at present, empirical default value has been still used in practice. In this study, the cross-sectional velocity distribution was calculated using an entropic method by utilizing the surface velocity distribution measured by STIV and compared with Acoustic Doppler Current Profiler (ADCP) observation. It was confirmed that the introduction of the velocity dip system express the flow velocity distribution in the vertical direction, where the velocity dip occurs due to the influence of vegetation.

scholarly journals Three-Dimensional Time Series Movement of the Cuolangma Glaciers, Southern Tibet with Sentinel-1 Imagery

2020 ◽  
Vol 12 (20) ◽  
pp. 3466
Author(s):  
Liye Yang ◽  
Chaoying Zhao ◽  
Zhong Lu ◽  
Chengsheng Yang ◽  
Qin Zhang
Keyword(s):  
Time Series ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Surface Velocity ◽  
Tibet Plateau ◽  
High Mountain ◽  
Southern Tibet ◽  
Central Himalayas ◽  
Glacier Velocity ◽  
Small Baseline

Many debris-covered glaciers are broadly distributed across High Mountain Asia and have made a number of contributions to water circulation for Qinghai-Tibet Plateau (QTP). The formation of large supraglacial lakes poses risks for glacier lake outburst floods (GLOFs). Therefore, it is important to monitor the movement of glaciers and to analyze their spatiotemporal characteristics. In this study we take Cuolangma glaciers in the central Himalayas as study targets, where glacier No.1 is a lake-terminating debris-covered glacier and glacier No.2 is a land-terminating debris-covered glacier. The 3D deformation time series is firstly estimated by using the Pixel Offset-Small Baseline Subsets (PO-SBAS) based on the ascending and descending Sentinel-1 datasets spanning from January to December 2018. Then the horizontal and vertical time series displacements are obtained to show their spatiotemporal features. The velocities of glacier No.1 in horizontal and vertical direction were up to 16.0 ± 0.04 m/year and 3.4 ± 0.42 m/year, respectively, and the ones of the glacier No.2 were 12.0 ± 0.07 m/year and 2.0 ± 0.27 m/year, respectively. Next, the correlation between the precipitation and the surface velocity suggests that the glacier velocity does not show a clear association with daily precipitation alone. Finally, the debris-covered glaciers evolution is evaluated which shows that the tongue of the glacier No.1 is wasting away and the transition of glacier No.2 from land-terminating to lake-terminating is a probable scenario in the later period of glacier wastage. This research can significantly serve for glacier multidimensional monitoring and the mitigation of hazardous disaster caused by debris-covered glaciers in the central Himalayas.

The behaviour of naturally oscillating three-dimensional flow around a cylinder

1978 ◽  
Vol 85 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Claude Tournier ◽  
Bernard Py
Keyword(s):  
Cross Section ◽  
Velocity Gradient ◽  
Three Dimensional ◽  
Surface Flow ◽  
Surface Velocity ◽  
Small Scale ◽  
Spanwise Direction ◽  
Wave System ◽  
Natural Oscillations ◽  
Stagnation Region

Split-film electrochemical transducer theory is briefly outlined so as to show its ability to separate statistical properties of each component of the surface velocity gradient in regions as different as a boundary layer, a separated zone and a three-dimensional separation line. A lot of measurements of the flow field near a cylinder which are not yet available elsewhere are carried out everywhere on the cross-section of a yawed cylinder. A direct verification of the independence principle and Wild's thermal analogy in separated zones is executed. The periodic and random parts of each component of the surface velocity gradient are separated. Cross-spectral analysis between any pair of points shows that the periodic surface flow is coherent upon any cross-section and in a large region in the spanwise direction. The stationary wave system is investigated in space and time. The reconstitution, instant by instant, of the averaged integral wall streamlines leads to an understanding of the synchronization of the natural oscillations. The four main stagnation or separation lines quickly move from one extreme position to the other, and at certain times contrary vortices stretching in the direction of the generators can appear. In the rearward stagnation region random small-scale fluctuations are probably turbulent, but in the intermediate region high-level random fluctuations in the spanwise direction are much more coherent and probably contribute to keeping the flow in phase at large distances.

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