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Paraz F, Bandi MM. Second order structure functions for higher powers of turbulent velocity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:484001. [PMID: 31387090 DOI: 10.1088/1361-648x/ab38ca] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We experimentally study the temporal second-order structure functions for integer powers of turbulent fluid velocity fluctuations [Formula: see text], in three dimensional (3D) and two dimensional (2D) turbulence. Here [Formula: see text] is a composite time-series constructed by averaging the concurrent time-series ([Formula: see text]) sampled at N spatially distributed Eulerian points. The N = 1 case has been extensively studied for velocity fluctuations (m = 1) and to a lesser extent for m > 1. The averaging method in case of N > 1 diverges from the Kolmogorov framework and has not been studied because fluctuations in [Formula: see text] are expected to smooth with increasing N leaving behind uninteresting large-scale mean flow information, but we find this is not so. We report the evolution of scaling exponents [Formula: see text] for [Formula: see text] in going from a single (N = 1) to a spatial average over several Eulerian points ([Formula: see text]). Our 3D experiments in a tank with rotating jets at the floor show [Formula: see text] for all m-values in agreement with prior results and evolves to an asymptotic value of [Formula: see text]. The evolution of [Formula: see text] follows the functional form [Formula: see text], where [Formula: see text] points is the only fit parameter representing the convergence rate constant. Results for the 2D experiments conducted in a gravity assisted soap film in the enstrophy cascade regime are in sharp contrast with their 3D counterparts. Firstly [Formula: see text] varies polynomially with m and asymptotes to a constant value at m = 5. Secondly, the evolution of [Formula: see text] is logarithmic [Formula: see text], where A and B are fit parameters and eventually deviates at large N and asymptotes to [Formula: see text] for all m. The starkly different convergence forms (exponential in 3D versus logarithmic in 2D) may be interpreted as a signature of inter-scale couplings in the respective turbulent flows by decomposing the two-point correlator for [Formula: see text] into a self-correlation and cross-correlation term. In addition to aiding in the theoretical development, the results may also have implications for determination of resolution in 2D turbulence experiments and simulations, wind energy and atmospheric boundary layer turbulence.
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Affiliation(s)
- F Paraz
- Nonlinear and Non-equilibrium Physics Unit, OIST Graduate University, Okinawa, 904-0495, Japan
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Gonçalves ND, Salvador HM, Fonte CP, Dias MM, Lopes JCB, Santos RJ. On the 2D nature of flow dynamics in opposed jets mixers. AIChE J 2016. [DOI: 10.1002/aic.15566] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Nelson D. Gonçalves
- Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials (LSRE‐LCM), Universidade do Porto, Faculdade de EngenhariaRua Dr. Roberto FriasPorto4200‐465 Portugal
| | - Hélder M. Salvador
- Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials (LSRE‐LCM), Universidade do Porto, Faculdade de EngenhariaRua Dr. Roberto FriasPorto4200‐465 Portugal
| | - Cláudio P. Fonte
- School of Chemical Engineering and Analytical ScienceThe University of ManchesterOxford RoadManchesterM13 9PL U.K
| | - Madalena M. Dias
- Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials (LSRE‐LCM), Universidade do Porto, Faculdade de EngenhariaRua Dr. Roberto FriasPorto4200‐465 Portugal
| | - José Carlos B. Lopes
- Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials (LSRE‐LCM), Universidade do Porto, Faculdade de EngenhariaRua Dr. Roberto FriasPorto4200‐465 Portugal
| | - Ricardo J. Santos
- Laboratory of Separation and Reaction Engineering – Laboratory of Catalysis and Materials (LSRE‐LCM), Universidade do Porto, Faculdade de EngenhariaRua Dr. Roberto FriasPorto4200‐465 Portugal
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Rivera MK, Ecke RE. Lagrangian statistics in weakly forced two-dimensional turbulence. CHAOS (WOODBURY, N.Y.) 2016; 26:013103. [PMID: 26826855 DOI: 10.1063/1.4937163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 11/20/2015] [Indexed: 06/05/2023]
Abstract
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.
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Affiliation(s)
- Michael K Rivera
- The Condensed Matter and Thermal Physics Group (MPA-10) and The Center for NonLinear Studies (T-CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Robert E Ecke
- The Condensed Matter and Thermal Physics Group (MPA-10) and The Center for NonLinear Studies (T-CNLS), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Nguyen Q, Srinivasan C, Papavassiliou DV. Flow-induced separation in wall turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:033019. [PMID: 25871214 DOI: 10.1103/physreve.91.033019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Indexed: 06/04/2023]
Abstract
One of the defining characteristics of turbulence is its ability to promote mixing. We present here a case where the opposite happens-simulation results indicate that particles can separate near the wall of a turbulent channel flow, when they have sufficiently different Schmidt numbers without use of any other means. The physical mechanism of the separation is understood when the interplay between convection and diffusion, as expressed by their characteristic time scales, is considered, leading to the determination of the necessary conditions for a successful separation between particles. Practical applications of these results can be found when very small particles need to be separated or removed from a fluid.
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Affiliation(s)
- Quoc Nguyen
- School of Chemical, Biological and Materials Engineering, The University of Oklahoma, 100 East Boyd St., SEC T-301, Norman, Oklahoma 73019, USA
| | - Chiranth Srinivasan
- School of Chemical, Biological and Materials Engineering, The University of Oklahoma, 100 East Boyd St., SEC T-301, Norman, Oklahoma 73019, USA
| | - Dimitrios V Papavassiliou
- School of Chemical, Biological and Materials Engineering, The University of Oklahoma, 100 East Boyd St., SEC T-301, Norman, Oklahoma 73019, USA
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Eyink GL, Benveniste D. Suppression of particle dispersion by sweeping effects in synthetic turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:023011. [PMID: 23496614 DOI: 10.1103/physreve.87.023011] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2012] [Indexed: 06/01/2023]
Abstract
Synthetic models of Eulerian turbulence like so-called kinematic simulations (KS) are often used as computational shortcuts for studying Lagrangian properties of turbulence. These models have been criticized by Thomson and Devenish (2005), who argued on physical grounds that sweeping decorrelation effects suppress pair dispersion in such models. We derive analytical results for Eulerian turbulence modeled by Gaussian random fields, in particular for the case with zero mean velocity. Our starting point is an exact integrodifferential equation for the particle pair separation distribution obtained from the Gaussian integration-by-parts identity. When memory times of particle locations are short, a Markovian approximation leads to a Richardson-type diffusion model. We obtain a time-dependent pair diffusivity tensor of the form K(ij)(r,t)=S(ij)(r)τ(r,t), where S(ij)(r) is the structure-function tensor and τ(r,t) is an effective correlation time of velocity increments. Crucially, this is found to be the minimum value of three times: the intrinsic turnover time τ(eddy)(r) at separation r, the overall evolution time t, and the sweeping time r/v(0) with v(0) the rms velocity. We study the diffusion model numerically by a Monte Carlo method. With inertial ranges like the largest achieved in most current KS (about 6 decades long), our model is found to reproduce the t(9/2) power law for pair dispersion predicted by Thomson and Devenish and observed in the KS. However, for much longer ranges, our model exhibits three distinct pair-dispersion laws in the inertial range: a Batchelor t(2) regime, followed by a Kraichnan-model-like t(1) diffusive regime, and then a t(6) regime. Finally, outside the inertial range, there is another t(1) regime with particles undergoing independent Taylor diffusion. These scalings are exactly the same as those predicted by Thomson and Devenish for KS with large mean velocities, which we argue hold also for KS with zero mean velocity. Our results support the basic conclusion of Thomson and Devenish (2005) that sweeping effects make Lagrangian properties of KS fundamentally differ from those of hydrodynamic turbulence for very extended inertial ranges.
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Affiliation(s)
- Gregory L Eyink
- Department of Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
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Liao Y, Kelley DH, Ouellette NT. Effects of forcing geometry on two-dimensional weak turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036306. [PMID: 23031012 DOI: 10.1103/physreve.86.036306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2012] [Indexed: 06/01/2023]
Abstract
Using high-resolution particle tracking velocimetry, we study the effects of the forcing geometry on the statistics of an electromagnetically stirred thin-layer flow. We consider two forcing arrangements: one that produces a lattice of vortices as a base flow, and one that produces an array of shear bands. We find that the vortex flow drives stronger fluctuating kinetic energy while the shear-band flow leads to more intense fluctuating velocity gradients. We explain our results by considering the spectral flow of energy in the system. Our results have implications for the design of two-dimensional flow experiments.
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Affiliation(s)
- Yang Liao
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
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von Kameke A, Huhn F, Fernández-García G, Muñuzuri AP, Pérez-Muñuzuri V. Double cascade turbulence and Richardson dispersion in a horizontal fluid flow induced by Faraday waves. PHYSICAL REVIEW LETTERS 2011; 107:074502. [PMID: 21902399 DOI: 10.1103/physrevlett.107.074502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2011] [Indexed: 05/31/2023]
Abstract
We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.
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Affiliation(s)
- A von Kameke
- Group of Nonlinear Physics, University of Santiago de Compostela, Spain.
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Akkermans RAD, Kamp LPJ, Clercx HJH, van Heijst GJF. Three-dimensional flow in electromagnetically driven shallow two-layer fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026314. [PMID: 20866912 DOI: 10.1103/physreve.82.026314] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2009] [Revised: 05/14/2010] [Indexed: 05/29/2023]
Abstract
Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the existence and evolution of complex three-dimensional (3D) flow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer fluid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. Remarkably, the experimental results, supported by the numerical simulations, show to a large extent the same 3D structures and evolution as in the single-layer case. The numerical simulations indicate that the so-called frontal circulation in the two-layer fluid is due to deformations of the internal interface. The 3D flow structures will also affect the distribution of massless passive particles released at the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity field is not divergence-free. This is in contrast with pure two-dimensional incompressible flows where the divergence of the velocity field is zero by definition.
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Affiliation(s)
- R A D Akkermans
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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Merrifield ST, Kelley DH, Ouellette NT. Scale-dependent statistical geometry in two-dimensional flow. PHYSICAL REVIEW LETTERS 2010; 104:254501. [PMID: 20867385 DOI: 10.1103/physrevlett.104.254501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2010] [Indexed: 05/29/2023]
Abstract
By studying the shape dynamics of three-particle clusters, we investigate the statistical geometry of a spatiotemporally chaotic experimental quasi-two-dimensional flow. We show that when shape and size are appropriately decoupled, these Lagrangian triangles assume statistically stationary shape distributions that depend on the flow scale, with smaller scales favoring more distorted triangles. These preferred shapes are not due to trapping by Eulerian flow structures. Since our flow does not have developed turbulent cascades, our results suggest that more careful work is required to understand the specific effects of turbulence on the advection of Lagrangian clusters.
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Affiliation(s)
- Sophia T Merrifield
- Department of Mechanical Engineering, Yale University, New Haven, Connecticut 06520, USA
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Ouellette NT, O'Malley PJJ, Gollub JP. Transport of finite-sized particles in chaotic flow. PHYSICAL REVIEW LETTERS 2008; 101:174504. [PMID: 18999753 DOI: 10.1103/physrevlett.101.174504] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2008] [Indexed: 05/27/2023]
Abstract
By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.
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Twardos MJ, Arratia PE, Rivera MK, Voth GA, Gollub JP, Ecke RE. Stretching fields and mixing near the transition to nonperiodic two-dimensional flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056315. [PMID: 18643169 DOI: 10.1103/physreve.77.056315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2007] [Revised: 04/02/2008] [Indexed: 05/26/2023]
Abstract
Although time-periodic fluid flows sometimes produce mixing via Lagrangian chaos, the additional contribution to mixing caused by nonperiodicity has not been quantified experimentally. Here, we do so for a quasi-two-dimensional flow generated by electromagnetic forcing. Several distinct measures of mixing are found to vary continuously with the Reynolds number, with no evident change in magnitude or slope at the onset of nonperiodicity. Furthermore, the scaled probability distributions of the mean Lyapunov exponent have the same form in the periodic and nonperiodic flow states.
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Affiliation(s)
- M J Twardos
- Condensed Matter & Thermal Physics Group and The Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Osborne DR, Vassilicos JC, Sung K, Haigh JD. Fundamentals of pair diffusion in kinematic simulations of turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036309. [PMID: 17025745 DOI: 10.1103/physreve.74.036309] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2005] [Revised: 03/20/2006] [Indexed: 05/12/2023]
Abstract
We demonstrate that kinematic simulation (KS) of three-dimensional homogeneous turbulence produces fluid element pair statistics in agreement with the predictions of L F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)] even though KS lacks explicit modeling of turbulent sweeping of small eddies by large ones. This scaling is most clearly evident in the turbulent diffusivity's dependence on rms pair separation and, to a lesser extent, on the pair's travel time statistics. It is also shown that kinematic simulation generates a probability density function of pair separation which is in good agreement with recent theory [S. Goto and J. C. Vassilicos, New J. Phys. 6, 65 (2004)] and with the scaling of the rms pair separation predicted by L. F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)]. Finally, the statistical persistence hypothesis (SPH) is formulated mathematically and its validity tested in KS. This formulation introduces the concept of stagnation point velocities and relates these to fluid accelerations. The scaling of accelerations found in kinematic simulation supports the SPH, even though KS does not generate a Kolmogorov scaling for the acceleration variance (except for a specific case and a limited range of outer to inner length-scale ratios). An argument is then presented that suggests that the stagnation points in homogeneous isotropic turbulence are on average long-lived.
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Affiliation(s)
- D R Osborne
- Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, Exhibition Road, London SW7 2BY, United Kingdom
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Celani A, Seminara A. Large-scale anisotropy in scalar turbulence. PHYSICAL REVIEW LETTERS 2006; 96:184501. [PMID: 16712366 DOI: 10.1103/physrevlett.96.184501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2006] [Indexed: 05/09/2023]
Abstract
The effect of anisotropy on the statistics of a passive tracer transported by a turbulent flow is investigated. We show that under broad conditions an arbitrarily small amount of anisotropy propagates to the large scales where it eventually dominates the structure of the concentration field. This result is obtained analytically in the framework of an exactly solvable model and confirmed by numerical simulations of scalar transport in two-dimensional turbulence.
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Affiliation(s)
- Antonio Celani
- INLN, CNRS, 1361 Route des Lucioles, 06560 Valbonne, France
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Rivera MK, Ecke RE. Lagrangian dynamics in two-dimensional turbulence. CHAOS (WOODBURY, N.Y.) 2005; 15:041108. [PMID: 16396584 DOI: 10.1063/1.2139969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Affiliation(s)
- Michael K Rivera
- Condensed Matter and Thermal Physics and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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