Analogy between predictions of Kolmogorov and Yaglom

Antonia, R. A.; Ould-Rouis, M.; Anselmet, Fabien; Zhu, Ye

doi:10.1017/s0022112096004090

Cited by 130 publications

(117 citation statements)

References 31 publications

Supporting

Mentioning

114

Contrasting

Order By: Relevance

“…An alternative derivation of this result using correlators instead of structure functions was also obtained in [14], and observed in numerical simulations [15]. When neutral fluid turbulence is considered, equation (3) becomes [11] |∆v| 2 ∆v = −4/3 ǫ r (ǫ being the average kinetic energy dissipation rate), from which Kolmogorov's -4/5 law for the longitudinal third order structure function can be recovered if there is full isotropy as (∆v ) 3 = −4/5 ǫ r.…”

mentioning

confidence: 77%

“…This transport is active as z ± and z ∓ are clearly not independent. Still, following the same procedure as in [11,12], and assuming local homogeneity, a relation similar to the Yaglom equation for the transport of a passive quantity [13] can be 1 obtained in the stationary stateHere, ∆z ± ≡ z ± (x ′ ) − z ± (x) are the (vector) increments of the fluctuations between two points x and x ′ ≡ x+r, ∇ and ∇ ′ are the gradients at the corresponding two points, ∂ is the longitudinal derivative along the separation r, while Y ± (r) are the mixed third order structure function |∆z ± | 2 ∆z ∓ and= 3ν |∂ z ± | 2 are the pseudo-energy average dissipation rates, namely the dissipation rates of both |z ± | 2 /2 respectively. Finally, ∆P represent the increment of the total pressure fluctuations and the kinematic viscosity ν is here assumed to be equal to the magnetic diffusivity κ (this last assumption is in fact not necessary if we concentrate on the inertial range, as we will do from now on).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Sorriso‐Valvo¹,

et al. 2007

View full text Add to dashboard Cite

We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.Space flights have shown that the interplanetary medium is permeated by a supersonic, highly turbulent plasma flowing out from the solar corona, the so called solar wind [1,2]. The turbulent character of the flow, at frequencies below the ion gyrofrequency f ci ≃ 1Hz, has been invoked since the first Mariner mission [3]. In fact, velocity and magnetic fluctuations power spectra are close to the Kolmogorov's -5/3 law [2,6]. However, even if fields fluctuations are usually considered within the framework of magnetohydrodynamic (MHD) turbulence [2], a firm established proof of the existence of an energy cascade, namely the main characteristic of turbulence, remains a conjecture so far [4]. This apparent lack could be fulfilled through the evidence for the existence of the only exact and nontrivial result of turbulence [6], that is a relation between the third order moment of the longitudinal increments of the fields and the separation [5]. This observation would firmly put low frequency solar wind fluctuations within the framework of MHD turbulence. The importance of such question stands beyond the understanding of the basic physics of solar wind turbulence. For example, it is well known that turbulence is one of the main obstacles to the confinement of plasmas in the fusion devices [7,8]. The understanding of interplanetary turbulence and its effects on energetic particle transport is of great importance also for Space Weather research [9], which is a relevant issue for spacecrafts and communication satellites operations, and for the security of human beings. Finally, more theoretical problems are concerned, such as the puzzle of solar coronal heating due to the turbulent flux toward small scales [10].Incompressible MHD equations are more complicated than the standard neutral fluid mechanics equations because the velocity of the charged fluid is coupled with the magnetic field generated by the motion of the fluid itself. However, written in terms of the Elsässer variables defined as z ± = v ± (4πρ) −1/2 b (v and b are the velocity and magnetic field respectively and ρ the mass density), they have the same structure as the Navier-Stokes equations [4]where P is the total hydromagnetic pressure, while ν is the viscosity and κ the magnetic diffusivity. In particular, the nonlinear term appears as z ∓ · ∇z ± , suggesting the form of a transport process, in which Alfvé...

show abstract

mentioning

confidence: 77%

mentioning

confidence: 99%

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Sorriso‐Valvo¹,

et al. 2007

View full text Add to dashboard Cite

show abstract

“…The viscous term of (1) can be neglected in the inertial range such that (1) reduces to 'Kolmogorov's 4/5 law', − (δu) 3 = (4/5) r, or equivalently, allowing for anisotropy [28], Figure 10 shows the approach of (δu)(δq) 2 n = − (δu)(δq) 2 /( r) to 4/3. At x/L 0 = 10.2, (δu)(δq) 2 n has a broad, flat peak with a maximum at 1.12, very near 4/3, while the peak of (δu)(δq) 2 n and its flatness diminish with x/L 0 .…”

Section: Scaling Range In the Spectra And Structure Functionsmentioning

confidence: 99%

Scale-by-scale energy budget in fractal element grid-generated turbulence

Hearst

Lavoie

2014

Journal of Turbulence

View full text Add to dashboard Cite

Measurements were conducted downstream of a square-fractal-element grid at Re L 0 = U L 0 /ν = 65, 000, where L 0 is the size of the largest element in the grid. The scale-byscale energy budget for grid turbulence is used to investigate the phenomenological change in the turbulence between the inhomogeneous and homogeneous regions downstream of the grid, providing greater insight into the evolution of the turbulence in these two regions. It is shown that in the far-field, x/L 0 ≥ 20, where the flow is approximately homogeneous and isotropic, the scale-by-scale energy budget proposed by Danaila et al.[1] for grid turbulence is well balanced. In the near-field, x/L 0 < 20, the same energy budget is not satisfied, with the imbalance of the budget occurring at scales in the range λ r L 0 . It is proposed that the imbalance is caused by non-zero transverse transport of turbulent kinetic energy and production due to transverse mean velocity gradients. Approach of the spectra to k −5/3 behaviour with a decade long scaling range in the inhomogeneous region is attributed to forcing by these non-zero transverse terms.

show abstract

“…Another relation between the second-and third-order structure functions was obtained by Antonia et al (1997) as…”

Section: Theoretical Considerationsmentioning

confidence: 99%