By P. Bradshaw
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An example is the simple physical argument, used above, that the smaller eddies will depend only on the mean energy transfer from the energy-containing eddies and not on the statistical properties of the latter. This cannot be quite correct: when discussing the smaller eddies we can define the "mean" energy transfer by an average over, say, 100 wavelengths or periods of the smaller eddies, and this average will itself vary at the much larger wavelength or period of the energy-containing eddies, so that the properties of the small-scale eddies have a "spotty" distribution in space and time.
10. The equation obtained by adding up all these terms and equating the sum to zero is the required conservation or "transport" equation for the turbulent energy or the sum of the Reynolds normal stresses. g. ref. 5, eqn. 10)]. Frequently, some of the terms can be neglected: usually, production and dissipation are the t The tensor form is — μ I—- + — - 1 which looks (but is not) half as large as 2 \ dxj dxi / the sum of the terms quoted here, because each term appears twice on summation. 28 TURBULENCE AND ITS MEASUREMENT largest although energy diffusion and advection outweigh them near the edge of a shear layer.
13), and finding the mean square of the output, u2(co) say, as if it were a complete signal :φ is then 1/dco times this mean square value. Turbulent fluctuations have a broad spectrum (Fig. 13): sometimes fairly flat peaks can be distinguished but discrete frequencies occur only in the earlier stages of transition from laminar to turbulent flow. The Equivalent rectangular band width Real band - pass filter Frequency -Energy-containing 0-1Γ Vi> 001 0001 k. B QQf. o r FIG. 13. Typical 4>2i(ki) wave number (or frequency) spectrum in boundary layer at about y/ô995 — 0*5.