By P. Bradshaw

ISBN-10: 0080166210

ISBN-13: 9780080166216

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Example text

Correlations with space and time delay are used in more detailed investigations of departures from Taylor's hypothesis in flows with high turbulent intensity. Note that the autocorrelation is always an even function (the same for positive and negative x) if the turbulence is statistically stationary in time: space correlations may be asymmetrical at large values; an asymmetrical (r, 0, 0) correlation implies that the turbulence is changing appreciably in an x distance equal to the size of the largest eddies, which in turn implies high Reynolds stress and turbulent intensity and, therefore, a departure from Taylor's hypothesis.

For the (American) National Committee for Fluid Motion Films, is an excellent introduction to the subject. I urge the reader of this book to do his own flow visualization, starting by watching clouds, rivers and smoke plumes to see how turbulence diffuses matter and momentum and tangles a line of fluid coming from a fixed source: even watching smoke from a cigarette helps to pass time in dull committee meetings. Turbulence is such a common phenomenon that there is no shortage of natural examples: however, some simple experiments can be even more informative, even to people with a good theoretical grounding in the subject.

When we speak of the length scale of the energy00 containing eddies we mean a length of order j Rar (actually called the "integral scale"). 4. Time Correlations (Autocorrelations or Autocovariances) The correlation between the same (Greek autos = self or same) fluctuating quantity measured at two different times (at the same point 30 TURBULENCE AND ITS MEASUREMENT in space) is not itself very relevant to the behaviour of turbulence and its measurement requires a time delay mechanism (usually a taperecorder with movable heads or a digital sample-and-delay system): the usual reason for interest is that if the turbulent velocity fluctuations are small compared with the mean velocity, the eddies or vortex lines do not change appreciably in shape as they pass a given point and therefore the autocorrelation of the v component (say) with time delay T, written as JR 2 2( T ) = KO v(* + r)lv2> will t>e the same as the space correlation with separation — JJx in the x direction (which we suppose for simplicity to be the direction of the mean velocity).

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An Introduction to Turbulence and its Measurement by P. Bradshaw


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