Scale-Dependent Statistical Geometry in Two-Dimensional Flow

Merrifield, Sophia; Kelley, Douglas H.; Ouellette, Nicholas T.

doi:10.1103/physrevlett.104.254501

Cited by 14 publications

(29 citation statements)

References 28 publications

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“…Our post-processing Matlab software is freely available. 25 In other work with higher-resolution cameras, we have routinely tracked as many as 30,000 particles per frame, 26 and an example of this sort of data is shown in Fig. 4.…”

Section: Methodsmentioning

confidence: 99%

Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment

Kelley

Ouellette

2011

American Journal of Physics

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A compact apparatus for muon lifetime measurement and time dilation demonstration in the undergraduate laboratory Am.Much of the drama and complexity of fluid flow occurs because its governing equations lack unique solutions. The observed behavior depends on the stability of the multitude of solutions, which can change with the experimental parameters. Instabilities cause sudden global shifts in behavior. We have developed a low-cost experiment to study a classical fluid instability. By using an electromagnetic technique, students drive Kolmogorov flow in a thin fluid layer and measure it quantitatively with a webcam. They extract positions and velocities from movies of the flow using Lagrangian particle tracking and compare their measurements to several theoretical predictions, including the effect of the drive current, the spatial structure of the flow, and the parameters at which instability occurs. The experiment can be tailored to undergraduates at any level or to graduate students by appropriate emphasis on the physical phenomena and the sophisticated mathematics that govern them.

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Section: Methodsmentioning

confidence: 99%

Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment

Kelley

Ouellette

2011

American Journal of Physics

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“…Statistics of triangle shape in the (

\overset{θ}{true}, γ

) space for (a and b) AVISO S 1, (c and d) S 2 drifters, and (e and f) S 1 drifters for the first 3 days. Figures a, c, and e show average trajectories superimposed on examples of triangle shapes (modified from Merrifield et al []). Black dots in Figures a, c, and e represent the diffusive limit.…”

Section: Metrics Of Triad Shape Analysismentioning

confidence: 99%

“…Several shape metrics have been proposed in the literature [e.g., Pumir et al, 2000;Cressman et al, 2004a]. Here following Merrifield et al [2010] and de Chaumont Quitry et al [2011], we use a two-parameter metric that has an intuitive interpretation for the case of triangles. We track shape evolution in ( , ) space, where is the largest internal angle of the triangle (ranging from ∕3 for equilateral triangles to for collinear vertices) and is the ratio of smallest to intermediate triangle sides (varying between 0 and 1).…”

Section: Metrics Of Triad Shape Analysismentioning

confidence: 99%

“…The evolution of triangles in 2‐D nondivergent flows has been studied numerically and experimentally in time‐dependent laminar (chaotic) flows [ Merrifield et al , ; de Chaumont Quitry et al , ] and turbulent flows [ Pumir et al , ; Biferale et al , ]. Consider initially equilateral triangles with sides l 1 = l 2 = l 3 , and renormalized “radius of gyration,”

R^{2} = \frac{1}{3} (l_{1}^{2} + l_{2}^{2} + l_{3}^{2})

, as previously defined by de Chaumont Quitry et al [].…”

Section: Introductionmentioning

confidence: 99%

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Submesoscale evolution of surface drifter triads in the Gulf of Mexico

Berta

Griffa

Özgökmen

et al. 2016

Geophysical Research Letters

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Triangle shape metrics are analyzed to quantify the evolution of submesoscale (100–500 m initial separation) surface drifter triplets released in the northern Gulf of Mexico. The observations are compared to synthetic drifters advected by geostrophic velocity fields derived from satellite altimetry. Observed submesoscale triads evolve rapidly, reaching highly elongated configurations on timescales of 6 h to 2 days, in contrast to 6 days or longer for altimetry‐derived synthetic data. Estimates of horizontal divergence and strain rate from the drifter triplets indicate the relative importance of divergence in the evolution of triangle shape. Horizontal divergence is scale dependent, on the order of the local Coriolis parameter, and 2 to 3 times larger for initial 100 m scales compared to initial 500 m scales.

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“…[1][2][3][4][5] The 2D turbulence and relative problems have attracted a lot of attentions in recent years. [6][7][8][9][10][11][12][13][14][15][16][17][18] Several review papers have been devoted to this topic in detail, for example, papers by Tabeling, 2 Kellay and Goldburg, 3 Boffetta and Ecke, 4 Bouchet and Venaille, 5 Van Heijst and Clercx, 19 to quote a few. The 2D Ekman-Navier-Stokes equation is written in terms of a single scalar vorticity field ω = ∇ × u as, i.e.,…”

Section: Introductionmentioning

confidence: 99%

Hilbert statistics of vorticity scaling in two-dimensional turbulence

Tan¹,

Huang²,

Meng³

2014

Physics of Fluids

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In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed ω(x, y) in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang transform, to a vorticity field obtained from a 81922 grid-points direct numerical simulation of the 2D turbulence with a forcing scale kf = 100 and an Ekman friction. The measured joint probability density function p(C, k) of mode Ci(x) of the vorticity ω and instantaneous wavenumber k(x) is separated by the forcing scale kf into two parts, which correspond to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional probability density function p(C|k) at given wavenumber k has an exponential tail. In the inverse energy cascade, the shape of p(C|k) does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent \documentclass[12pt]{minimal}\begin{document}$\zeta _{\omega }^I(q)$\end{document}ζωI(q) is linear with the statistical order q, i.e., \documentclass[12pt]{minimal}\begin{document}$\zeta _{\omega }^I(q)=-q/3$\end{document}ζωI(q)=−q/3, confirming the nonintermittent cascade process. In the forward enstrophy cascade, the core part of p(C|k) is changing with wavenumber k, indicating an intermittent forward cascade. The measured scaling exponent \documentclass[12pt]{minimal}\begin{document}$\zeta _{\omega }^F(q)$\end{document}ζωF(q) is nonlinear with q and can be described very well by a log-Poisson fitting: \documentclass[12pt]{minimal}\begin{document}$\zeta _{\omega }^F(q)=\frac{1}{3}q+0.45\left( 1-0.43^{q}\right)$\end{document}ζωF(q)=13q+0.451−0.43q. However, the extracted vorticity scaling exponents ζω(q) for both inverse energy cascade and forward enstrophy cascade are not consistent with Kraichnan's theory prediction. New theory for the vorticity field in 2D turbulence is required to interpret the observed scaling behavior.

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Scale-Dependent Statistical Geometry in Two-Dimensional Flow

Cited by 14 publications

References 28 publications

Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment

Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment

Submesoscale evolution of surface drifter triads in the Gulf of Mexico

Hilbert statistics of vorticity scaling in two-dimensional turbulence

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