By Dieter Biskamp
Publisher: Cambridge University Press
Print Publication Year: 2003
Online Publication Date:August 2009
Online ISBN:9780511535222
Hardback ISBN:9780521810111
Paperback ISBN:9780521052535
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535222.008
Subjects: Plasma Physics and Fusion Physics, Astrophysics
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Turbulence is usually associated with the idea of self-similarity, which means that the spatial distribution of the turbulent eddies looks the same on any scale level in the inertial range. This is a basic assumption in the Kolmogorov phenomenology K41 and, on the same lines, the IK phenomenology introduced in Section 5.3.2. It is, however, well known that this picture is not exactly true, since it ignores the existence of small-scale structures, which cannot be distributed in a uniform space-filling way. In fact, in a real turbulence field experiments as well as numerical simulations show that smaller eddies, or higher frequencies, become increasingly sparse, or intermittent, which apparently violates self-similarity. This chapter deals with the various aspects of intermittency.
Section 7.1 gives a brief introduction. We illustrate the concept of self-similarity by some simple examples and clarify the notion of intermittency, distinguishing between dissipation-range and inertial-range intermittency. Section 7.2 deals with structure functions, in particular the set of inertial-range scaling exponents, which are convenient parameters for a quantitative description of the statistical distribution of the turbulence scales. We discuss the important constraints on these exponents imposed by basic probabilistic requirements. Since experiments and, even more so, numerical simulations deal with turbulence of finite, often rather low, Reynolds number, the scaling range may be quite short, or even hardly discernable, especially for higher-order structure functions, which makes determination of the scaling exponents difficult. The scaling properties can, however, be substantially improved by making use of the extended self-similarity (ESS), which often provides surprisingly accurate values of the relative scaling exponents.
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2 - Magnetohydrodynamics : Read PDF
pp. 10-32
3 - Transition to turbulence : Read PDF
pp. 33-64
4 - Macroscopic turbulence theory : Read PDF
pp. 65-85
5 - Spectral properties and phenomenology : Read PDF
pp. 86-112
6 - Two-point-closure theory : Read PDF
pp. 113-130
pp. 131-160
8 - Two-dimensional turbulence : Read PDF
pp. 161-182
9 - Compressible turbulence and turbulent convection : Read PDF
pp. 183-216
10 - Turbulence in the solar wind : Read PDF
pp. 217-232
11 - Turbulence in accretion disks : Read PDF
pp. 233-255
12 - Interstellar turbulence : Read PDF
pp. 256-274
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