By P. Bradshaw
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Extra resources for An Introduction to Turbulence and its Measurement
28 TURBULENCE AND ITS MEASUREMENT largest although energy diffusion and advection outweigh them near the edge of a shear layer. The equation can be regarded as an equation for the rate of change of \$q2 along a mean streamline in terms of local quantities: the actual value of q2 would have to be obtained by integrating the equation along the whole length of the mean streamline, starting at the point where it entered the region of turbulent flow. In non-mathematical language, q2 depends on the whole history of the flow, in particular the history of the mean rate of strain which appears in the production terms [(3) above].
Since w(x) v(x + r) is not in general an even function of r, it is not equal to w(x + r) v(x) and the two must be measured separately; in special cases symmetries can be distinguished. Wave number spectra can be derived as the Fourier transforms of these and other cross-correlations. 9. g. those like w(x) v(x) v(x + r) transform into spectra giving the energy transfer from low wave numbers to high wave numbers]. Correlations of the fourth and higher orders are bound to be partly degenerate because there are only three velocity components to choose from.
The only quantities that appreciately influence the flow close to the solid surface are expected to be the shear stress at the wall, T W , the fluid properties, say ρ and v, and the distance from the wall itself.
An Introduction to Turbulence and its Measurement by P. Bradshaw