Measures of Anisotropy and the Universal Properties of Turbulence

Kurien, Susan; Sreenivasan, Katepalli R.

doi:10.1007/3-540-45674-0_2

Cited by 37 publications

(47 citation statements)

References 23 publications

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“…The concept of averaging over the sphere in order to extract the isotropic component of turbulence data has existed for some time [15,16]. Present high-Reynolds number experiments provide limited data -often only a few spatial points of data acquisition, with vector increment directions limited by the location of the probes and the implementation of a suitable space-time surrogation (Taylor's hypothesis).…”

Section: Introductionmentioning

confidence: 99%

Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law

2003

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One of the main benchmarks in direct numerical simulations of three-dimensional turbulence is the Kolmogorov 1941 prediction for third-order structure functions with homogeneous and isotropic statistics in the infinite-Reynolds number limit. Previous DNS techniques to obtain isotropic statistics have relied on time-averaging structure functions in a few directions over many eddy turnover times, using forcing schemes carefully constructed to generate isotropic data. Motivated by recent theoretical work which removes isotropy requirements by spherically averaging structure functions over all directions, we will present results which supplement long-time averaging by angleaveraging over up to 73 directions from a single flow snapshot. The directions are among those natural to a square computational grid, and are weighted to approximate the spherical average.The averaging process is cheap, and for the Kolmogorov 1941 4/5ths law, reasonable results can be obtained from a single snapshot of data. This procedure may be used to investigate the isotropic statistics of any quantity of interest.

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Section: Introductionmentioning

confidence: 99%

Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law

2003

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“…These old studies have been used to investigate the spectral properties of the secondorder tensor components, and to investigate the radial evolution of anisotropy. Here we investigate the scaling properties of anisotropy of the interplanetary magnetic field, by using the data analysis technique described extensively in Ref.s [5,6] and [3]. This technique allows us to define the scaling properties of anisotropy of the interplanetary space fluctuations, as far as scaling exponents of high-order tensors are considered, so that intermittency is considered.…”

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confidence: 99%

“…At variance with Ref. [12], since S α1,α2,···,αn (r) display multiple power-law scaling, we prefer to fit the structure functions by the following Batchelor relation [5,6,22] S α1,···,αn (r) = A α1,···,αn η n (r/η)…”

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confidence: 99%

“…The multiple power-law behavior of the structure functions is described by equation (2) through the exponent C α1,α2,···,αn , which are the scaling parameters obtained from the fit of the data corresponding to the inertial range scaling, such that the usual scaling exponent can be recovered as ζ α1,···,αn = n − 2C α1,···,αn [5,6]. This can easily be tested by dividing the structure functions by the factor [1 + D α1,···,αn (r/L 0 )] 2Cα 1 ,···,αn −n , and observing the powerlaw behavior, with exponent ζ α1,···,αn , of the resulting extended structure function.…”

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confidence: 99%

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Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

et al. 2006

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Abstract. -The anisotropy of magnetophydrodynamic turbulence is investigated by using solar wind data from the Helios 2 spacecraft. We investigate the behaviour of the complete high-order moment tensors of magnetic field increments and we compare the usual longitudinal structure functions which have both isotropic and anisotropic contributions, to the fully anisotropic contribution. Scaling exponents have been extracted by an interpolation scaling function. Unlike the usual turbulence in fluid flows, small-scale magnetic fluctuations remain anisotropic. We discuss the radial dependence of both anisotropy and intermittency and their relationship.The idea that small scales were statistically isotropic to a high degree, in spite of the anisotropy of large scales, is at the heart of the concept of universality underlying scaling behaviour in turbulent fluid flow [1]. As experiments became increasingly sophisticated, evidence for the presence of anisotropy for both scalar fields [2] and velocity fields [3] has grown up. To what extent scaling laws extracted from experiments are approximated by the scaling laws obtained from (isotropic) cascade models [4], became an urgent issue. A workable benchmark is represented by the following conjecture [5,6]. Suppose that for a given statistical measurable quantity, scaling features can be splitted into an isotropic and an anisotropic part. We might ask to what extent the ratio between the anisotropic and the isotropic part vanishes as the scale goes down. Of course if we are able to define quantities for which the isotropic part is exactly zero, we can measure scaling laws related entirely to the anisotropic part. A formal analysis to reveal the isotropic and anisotropic contributions to structure functions can be performed by considering their SO(3) decomposition [7]. This is based in a foliation of various j-sectors of the linear space generated by the structure functions. For a recent review on anisotropy in turbulent flows see [8].c EDP Sciences

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“…Kurien and Sreenivasan, 2000) the following important scales of the reconnection flow dynamics can be estimated: 1) Energy input scale. If found in observed spectra it would give us an estimation of the transversal dimensions of outflow.…”

Section: Discussionmentioning

confidence: 99%

Diagnostics of solar flare reconnection

Karlický

Bárta

2004

Nonlin. Processes Geophys.

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Abstract. We present new diagnostics of the solar flare reconnection, mainly based on the plasma radio emission. We propose that the high-frequency (600-2000 MHz) slowly drifting pulsating structures map the flare magnetic field reconnection. These structures correspond to the radio emission from plasmoids which are formed in the extended current sheet due to tearing and coalescence processes. An increase of the frequency drift of the drifting structures is interpreted as an increase of the reconnection rate. Using this model, time scales of slowly drifting pulsating structure observed during the 12 April 2001 flare by the Trieste radiopolarimeter with high time resolution (1 ms) are interpreted as a radio manifestation of electron beams accelerated in the multi-scale reconnection process. For short periods Fourier spectra of the observed structure have a power-law form with power-law indices in the 1.3-1.6 range. For comparison the 2-D MHD numerical modeling of the multi-scale reconnection is made and it is shown that Fourier spectrum of the reconnection dissipation power has also a power-law form, but with power-law index 2. Furthermore, we compute a time evolution of plasma parameters (density, magnetic field etc) in the 2-D MHD model of the reconnection. Then assuming a plasma radio emission from locations, where the "doubleresonance" instability generates the upper-hybrid waves due to unstable distribution function of suprathermal electrons, we model radio spectra. Effects of the MHD turbulence are included. The resulting spectra are compared with those observed. It is found, that depending on model parameters the lace bursts and the decimetric spikes can be reproduced. Thus, it is shown that the model can be used for diagnostics of the flare reconnection process. We also point out possible radio signatures of reconnection outflow termination shocks. They are detected as type II-like herringbone structures in the 200-700 MHz frequency range. Finally, we mention Hα spectra of the 18 September 1995 eruptive prominence which indicate the bi-directional plasma flow as expected in the reconnection process.

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Measures of Anisotropy and the Universal Properties of Turbulence

Cited by 37 publications

References 23 publications

Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law

Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law

Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

Diagnostics of solar flare reconnection

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