The non-local nature of structure functions

Krogstad, P. A. and Davidson, P. A. (2007). The non-local nature of structure functions. In: Peter Jacobs, Tim McIntyre, Matthew Cleary, David Buttsworth, David Mee, Rose Clements, Richard Morgan and Charles Lemckert, 16th Australasian Fluid Mechanics Conference (AFMC). 16th Australasian Fluid Mechanics Conference (AFMC), Gold Coast, Queensland, Australia, (545-550). 3-7 December, 2007.

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Author Krogstad, P. A.
Davidson, P. A.
Title of paper The non-local nature of structure functions
Conference name 16th Australasian Fluid Mechanics Conference (AFMC)
Conference location Gold Coast, Queensland, Australia
Conference dates 3-7 December, 2007
Proceedings title 16th Australasian Fluid Mechanics Conference (AFMC)
Place of Publication Brisbane, Australia
Publisher School of Engineering, The University of Queensland
Publication Year 2007
Year available 2007
Sub-type Fully published paper
ISBN 978-1-864998-94-8
Editor Peter Jacobs
Tim McIntyre
Matthew Cleary
David Buttsworth
David Mee
Rose Clements
Richard Morgan
Charles Lemckert
Start page 545
End page 550
Total pages 5
Collection year 2007
Language eng
Abstract/Summary Kolmogorov’s two-thirds, h(Dv)2i e2/3r2/3, and five-thirds, E e2/3k−5/3, laws are formally equivalent in the limit of vanishing viscosity, n!0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s2/3, in accordance with Kolmogorov’s 1941 law, and we vary the range of scales, g = smax/smin, in any one realisation from g = 25 to g = 800. This is equivalent to varying the Reynolds number in an experiment from Rl = 60 to Rl = 600. While there is some evidence of a five-thirds law for g > 50 (Rl > 100), the two-thirds law only starts to become apparent when g approaches 200 (Rl 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, h(Dv)2i takes the form of a mixed power-law, a1+a2r2+a3r2/3, where a2r2 tracks the variation in enstrophy and a3r2/3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r2/3 law by the enstrophy contribution, a2r2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency. (See also [2].)
Subjects 290501 Mechanical Engineering
290600 Chemical Engineering
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status Unknown

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Created: Wed, 19 Dec 2007, 12:30:48 EST by Laura McTaggart on behalf of School of Engineering