ZERO CROSSINGS OF VELOCITY FLUCTUATIONS IN TURBULENT BOUNDARY-LAYERS

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 R(lambda)-1/2, where R(lambda) is the Reynolds number based on the Taylor microscale, lambda. The pdf's for the normal velocity component u 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.