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By P. Bradshaw
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Additional resources for An Introduction to Turbulence and its Measurement
This vorticity is stretched, and turned towards the direction of motion, as the flow rounds the corner. This mean vortex stretching accounts for the great complication of three-dimensional flows, whether laminar or turbulent. Between them, these simple experiments demonstrate most of the qualitative features of turbulence described in this book. In particular, they should convince the reader of the need to study turbulence by statistical means, and of the essential implausibility of simple formulae purporting to explain this complicated phenomenon.
A scalar) is u2 + v2 + w2, written as q2 for brevity and to show that it is the mean square of the resultant velocity fluctuation q. The sum of the principal stresses is — qq2, and \qq2 is called the turbulent (kinetic) energy per unit volume. The justification for the name is that we can deduce, from the Navier-Stokes equations, a conservation equation for the value of \qq2 in the elementary control volume of Fig. 10 and identify the terms with quantities representing sources or sinks of energy or with "transport" of energy in or out of the control volume.
FIG. 11. 5. Physically, the correlation with separation r is a measure of the strength of eddies whose length in the direction of the vector r is greater than the magnitude of r (since eddies smaller than this will not contribute to the correlation): as a warning that this is an imprecise concept, note that the correlations for the three velocity components will in general be different for the same r. 4. 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").