On Reynolds Averaging of Turbulence Time Series |
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Authors: | George Treviño Edgar L Andreas |
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Institution: | (1) CHIRES, Inc., P.O. Box 201481, San Antonio, TX 78220-8481, USA;(2) North West Research Associates, Inc. (Seattle Division), 25 Eagle Ridge, Lebanon, NH 03766-1900, USA |
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Abstract: | We show that validity of Reynolds averaging for estimating the (ensemble) mean of a turbulence time series requires that the
series values be both stationary and uncorrelated. In strict statistical terminology, these two conditions are jointly designated as independent identically distributed (i.i.d.). Moreover, we show that when the series values are correlated, knowledge of the correlation between the values is needed
to obtain a reliable estimate of the mean. Last, we contend that a viable averaging algorithm must be Reynolds number (Re) dependent, requiring one version for low Re (Gaussian) turbulence and another for high Re (non-Gaussian) turbulence. Alternatively the median (as opposed to the mean) is recommended as a measure of the central tendency of the turbulence probability density function. |
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Keywords: | Correlated data Non-Gaussian turbulence Time averaging |
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