Zero crossings of velocity fluctuations in turbulent boundary layers

Abstract

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.

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

“…[21,22]). It turns out that the average length is proportional to the Taylor microscale, and this is true for any random signal that obeys a Gaussian probability density function.…”

Scale Distributions and Fractal Dimensions in Turbulence

“…The corresponding spacing pdf was reported as described by Poisson statistics from measurements in turbulent boundary layers [14,15], with constant fractal dimensions reported for such data [2]. For a Poisson point process, i.e., p 1 ͑l͒dl exp͑2l͞l m ͒dl͞l m , however, the dimension is [cf.…”

Cover illustration: Non-premixed hydrocarbon flame

“…This has been an active area of research, some of which supports the proposal that (power-law) fractal analysis is applicable to the description of isosurfaces in turbulence [7][8][9][10][11][12][13], while other work suggests a scale-dependent fractal behaviour [14][15][16][17][18][19]. Extensions to the original fractal framework were recently proposed to accommodate the more general behaviour that has been observed [20][21][22].…”