scholarly journals On velocity structure functions and the spherical vortex model for isotropic turbulence

2001 ◽  
Vol 13 (7) ◽  
pp. 2019-2029 ◽  
Author(s):  
Keri A. Aivazis ◽  
D. I. Pullin
Keyword(s):  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Structure Functions ◽  
Vortex Model ◽  
Spherical Vortex

Pressure structure functions and spectra for locally isotropic turbulence

1995 ◽  
Vol 296 ◽  
pp. 247-269 ◽  
Author(s):  
Reginald J. Hill ◽  
James M. Wilczak
Keyword(s):  
Pressure Gradient ◽  
Structure Function ◽  
Fourth Order ◽  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Structure Functions ◽  
Inertial Range ◽  
Previous Theory ◽  
Local Isotropy

Beginning with the known relationship between the pressure structure function and the fourth-order two-point correlation of velocity derivatives, we obtain a new theory relating the pressure structure function and spectrum to fourth-order velocity structure functions. This new theory is valid for all Reynolds numbers and for all spatial separations and wavenumbers. We do not use the joint Gaussian assumption that was used in previous theory. The only assumptions are local homogeneity, local isotropy, incompressibility, and use of the Navier–Stokes equation. Specific formulae are given for the mean-squared pressure gradient, the correlation of pressure gradients, the viscous range of the pressure structure function, and the pressure variance. Of course, pressure variance is a descriptor of the energy-containing range. Therefore, for any Reynolds number, the formula for pressure variance requires the more restrictive assumption of isotropy. For the case of large Reynolds numbers, formulae are given for the inertial range of the pressure structure function and spectrum and of the pressure-gradient correlation; these are valid on the basis of local isotropy, as are the formulae for mean-squared pressure gradient and the viscous range of the pressure structure function. Using the experimentally verified extension to fourth-order velocity structure functions of Kolmogorov's theory, we obtain r4/3 and k−7/3 laws for the inertial range of the pressure structure function and spectrum. The modifications of these power laws to account for the effects of turbulence intermittency are also given. New universal constants are defined; these require experimental evaluation. The pressure structure function is sensitive to slight departures from local isotropy, implying stringent conditions on experimental data, but applicability of the previous theory is likewise constrained. The results are also sensitive to compressibility.

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

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