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.

Lagrangian frequency spectra of vertical velocity and vorticity in high-Reynolds-number oceanic turbulence

1998 ◽  
Vol 362 ◽  
pp. 177-198 ◽  
Author(s):  
REN-CHIEH LIEN ◽  
ERIC A. D'ASARO ◽  
GEOFFREY T. DAIRIKI
Keyword(s):  
Turbulent Flows ◽  
Frequency Spectrum ◽  
Finite Size ◽  
Inertial Subrange ◽  
Substantial Part ◽  
Spatial Average ◽  
Vertical Acceleration ◽  
Frequency Range ◽  
Frequency Spectra ◽  
Large Eddy

Lagrangian properties of oceanic turbulent boundary layers were measured using neutrally buoyant floats. Vertical acceleration was computed from pressure (depth) measured on the floats. An average vertical vorticity was computed from the spin rate of the float. Forms for the Lagrangian frequency spectra of acceleration, ϕa(ω), and the Lagrangian frequency spectrum of average vorticity are found using dimension analysis. The flow is characterized by a kinetic energy dissipation rate, ε, and a large-eddy frequency, ω0. The float is characterized by its size. The proposed non-dimensionalization accurately collapses the observed spectra into a common form. The spectra differ from those expected for perfect Lagrangian measurements over a substantial part of the measured frequency range owing to the finite size of the float. Exact theoretical forms for the Lagrangian frequency spectra are derived from the corresponding Eulerian wavenumber spectra and a wavenumber–frequency distribution function used in previous numerical simulations of turbulence. The effect of finite float size is modelled as a spatial average. The observed non-dimensional acceleration and vorticity spectra agree with these theoretical predictions, except for the high-frequency part of the vorticity spectrum, where the details of the float behaviour are important, but inaccurately modelled. A correction to the exact Lagrangian acceleration spectra due to measurement by a finite-sized float is thus obtained. With this correction, a frequency range extending from approximately one decade below ω0 to approximately one decade into the inertial subrange can be resolved by the data. Overall, the data are consistent with the proposed transformation from the Eulerian wavenumber spectrum to the Lagrangian frequency spectrum. Two parameters, ε and ω0, are sufficient to describe Lagrangian spectra from several different oceanic turbulent flows. The Lagrangian Kolmogorov constant for acceleration, βa≡ϕa/ε, has a value between 1 and 2 in a convectively driven boundary layer. The analysis suggests a Lagrangian frequency spectrum for vorticity that is white at all frequencies in the inertial subrange and below, and a Lagrangian frequency spectrum for energy that is white below the large-eddy scale and has a slope of −2 in the inertial subrange.

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 Vortex identification in turbulent flows past plates using the Lagrangian method

2019 ◽  
Vol 97 (8) ◽  
pp. 895-910
Author(s):  
Bashar Attiya ◽  
I-Han Liu ◽  
Muhannad Altimemy ◽  
Cosan Daskiran ◽  
Alparslan Oztekin
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Spatial Location ◽  
High Fidelity ◽  
Vortex Identification ◽  
Finite Time Lyapunov Exponent ◽  
Large Eddy ◽  
Spatial And Temporal Characteristics

Vortex identifications in turbulent flows past arrays of tandem plates are performed by employing the velocity field obtained by high-fidelity large eddy simulations. Lagrangian coherent structures (LCSs) are extracted to examine the evolution and the nonlinear interaction of vortices and to characterize the spatial and temporal characteristics of the flow. LCSs’ identification method is based on the finite-time Lyapunov exponent (FTLE), which is evaluated using the instantaneous velocity data. The simulations are performed in three-dimensional geometries to understand the physics of fluid motion and the vortex dynamics in the vicinity of plates and surfaces at Reynolds number of 50 000. The instantaneous vorticity fields, Eulerian Q-criterion, and LCSs are presented to interpret and understand complex turbulent flow structures. The three-dimensional FTLE fields provide valuable information about the vortex generation, spatial location, evolution, shedding, decaying, and dissipation of vortices. It is demonstrated here that FTLE can be used together with Eulerian vortex identifiers to characterize the turbulent flow field effectively.

scholarly journals Lagrangian Transport and Chaotic Advection in Three-Dimensional Laminar Flows

2021 ◽  
Author(s):  
Michel F. M. Speetjens ◽  
Guy Metcalfe ◽  
Murray Rudman
Keyword(s):  
Turbulent Flows ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Chaotic Advection ◽  
Systematic Analysis ◽  
Lagrangian Transport ◽  
Analysis And Design ◽  
Efficient Transport ◽  
Transport And Mixing

Abstract Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. Turbulent flows promote efficient transport and mixing by their inherent randomness. Laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion ("advection") and the geometry, topology and coherence of fluid trajectories. Efficient laminar transport being equivalent to "chaotic advection" is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows yet the real world is three dimensional (3D). Second, Lagrangian transport is typically investigated for idealised flows yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilisation of know-how on 3D Lagrangian transport and its dissemination to practice. To this end 3D practical flows are categorised into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the "Lagrangian mindset" into the analysis and design of 3D practical flows.

scholarly journals Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Entrance Slot

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1079
Author(s):  
Lena Mahl ◽  
Patrick Heneka ◽  
Martin Henning ◽  
Roman B. Weichert
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Free Water ◽  
Lateral Wall ◽  
Lateral Spreading ◽  
Propagation Length ◽  
Vertical Slot ◽  
Surface Jets

The efficiency of a fishway is determined by the ability of immigrating fish to follow its attraction flow (i.e., its jet) to locate and enter the fishway entrance. The hydraulic characteristics of fishway entrance jets can be simplified using findings from widely investigated surface jets produced by shaped nozzles. However, the effect of the different boundary conditions of fishway entrance jets (characterized by vertical entrance slots) compared to nozzle jets must be considered. We investigate the downstream propagation of attraction jets from the vertical slot of a fishway entrance into a quiescent tailrace, considering the following boundary conditions not considered for nozzle jets: (1) slot geometry, (2) turbulence characteristics of the approach flow to the slot, and (3) presence of a lateral wall downstream of the slot. We quantify the effect of these boundary conditions using three-dimensional hydrodynamic-numeric flow simulations with DES and RANS turbulence models and a volume-of-fluid method (VoF) to simulate the free water surface. In addition, we compare jet propagation with existing analytical methods for describing jet propagations from nozzles. We show that a turbulent and inhomogeneous approach flow towards a vertical slot reduces the propagation length of the slot jet in the tailrace due to increased lateral spreading compared to that of a jet produced by a shaped nozzle. An additional lateral wall in the tailrace reduces lateral spreading and significantly increases the propagation length. For highly turbulent flows at fishway entrances, the RANS model tends to overestimate the jet propagation compared to the transient DES model.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

Secondary motion in convection layers generated by lateral heating of a solute gradient

2002 ◽  
Vol 455 ◽  
pp. 1-19 ◽  
Author(s):  
CHO LIK CHAN ◽  
WEN-YAU CHEN ◽  
C. F. CHEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Convection Cell ◽  
Experimental Conditions ◽  
Longitudinal Plane ◽  
Secondary Motion ◽  
Solute Gradient

The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual ow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.

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