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The issue of experimental determination of the intermittency exponent μ, is revisited and it is shown that the ‘‘best’’ estimate for it is 0.25±0.05. This ‘‘best’’ estimate is obtained from recent atmospheric data, and is based on several different techniques.

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Using velocity data obtained in the atmospheric surface layer, we examine Kolmogorov's refined hypotheses. In particular, we focus on the properties of the stochastic variable K=Aw(r)/(re r ) ,/3 , where Auir) is the velocity increment over a distance r, and e r is the dissipation rate averaged over linear intervals of size r. We show that V has an approximately universal probability density function for r in the inertial range and discuss its properties; we also examine the properties of V for r outside the inertial range.PACS numbers: 05.45.+b, 02.50,+s, 03.40.Gc, A fruitful idea in high-Reynolds-number turbulence is the phenomenological picture of local structure introduced by Kolmogorov [1]. In its simplified version, the picture relates to the probability density function (PDF) of the velocity increment Aw (/*) = u (x + r) -u (x), where u (x+r) and uix) are velocities along the x axis at two points x and x +r separated by a distance r<^L, L being the integral scale of turbulence. According to the first hypothesis, the PDF of Auir) depends (besides on r itself) only on the average rate of energy dissipation (e) and the fluid viscosity v. The second hypothesis is that if the Reynolds number is very large, there exists a range of scales (the so-called inertial range) for which v becomes irrelevant, so that the only important external parameter is (s). The consequences of these universality arguments are well known [2] and need no repetition. Reference [2] also describes the circumstances which led to the modification of these hypotheses.Kolmogorov [3] himself introduced refinements of his 1941 theory, which abandoned local universality and introduced more restrictive alternatives to the 1941 hypotheses. The first refined hypothesis postulated a certain relation between Au(r) and the local average of the energy dissipation rate e r (x,t), taken over an interval of size r centered at x. Define, following Kolmogorov [3], a velocity scale at the point (x,t) by U r = (re r ) l/3 and form the local Reynolds number as Re r =t/ r r/v.(1)The first refined hypothesis then takes the form of the statement that, for r<£L,where V is a stochastic variable whose PDF depends only on Re r . The second refined hypothesis states that, if Re r^> 1, the PDF of V becomes independent also of Re r and thus universal. Unlike the original hypotheses, these refinements require a supplementary statement on the PDF of Au(r) or of e r . Kolmogorov's third hypothesis is that the PDF of e r is log-normal with a specific form for its variance. The consequences of Eq.(2) have been tested in vari-ous ways, but mainly by viewing it as a dimensional relation |Aw(r)|~(re r ) 1/3 . The stochastic function V is usually disregarded, often leading to misinterpretations of Eq.(2). Indeed, V contains much of the inertial range physics. For example, if Kolmogorov's j law [4]is understood to express the cascade of turbulent kinetic energy from large to small scales, the nonzero value of (K 3 > should account for this process. Similarly, the knowledge of t...

In this paper some results are presented on the statistical properties of zero crossings of turbulent velocity fluctuations in boundary layers over a wide range of Reynolds numbers. The earlier finding that the probability density function (pdf) of the intervals between successive zero crossings of the streamwise velocity fluctuation u can be approximated by two exponentials, each with its own characteristic scale, is confirmed. The cross-stream variation of these characteristic scales is investigated. One of these scales, corresponding to the large zero-crossing intervals, is independent of the Reynolds number, while the other for the viscous-dominated small-scale crossings varies with as Rλ−1/2, where Rλ is the Reynolds number based on the Taylor microscale, λ. The pdf’s for the normal velocity component v and the fluctuating part of the Reynolds stress uv are essentially exponential over the whole range of zero-crossing scales, and each possesses just one characteristic scale. The mean and the standard deviation of the zero-crossing scales of u and v, when normalized by their respective Taylor microscales, are roughly unity and essentially independent of the cross-stream position. Similar data are also presented for the Reynolds stress fluctuations. A brief discussion of the results as well as an example of the application of the zero-crossing pdf are given.