An Introduction to Turbulence and Its Measurement: by P. Bradshaw

By P. Bradshaw

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Extra resources for An Introduction to Turbulence and Its Measurement: Thermodynamics and Fluid Mechanics Series (C.I.L.)

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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].

Therefore the flows described below are to be regarded as building bricks for the synthesis of more complicated flows, as well as simple educational examples. Experimental results in idealized shear flows are reviewed by Townsend,(5) and I have given references to more recent research reports in the "Further Reading" list so that readers who are interested in quantitative results for particular flows can study them in context. The present book is not the place for a critical analysis of experimental results and I am unwilling to present the results without such analysis.

Its Fourier transform is the frequency spectrum of ΰν, which can be measured directly by putting the u and v signals through separate but identical band pass filters! a n d taking the mean product of the two outputs, u(co) and ν(ω), say. s. signals occasionally feel that since the spectrum φ(ω) of y/u2 is [u(œ)]2 the spectrum of uv should be u2(œ)v2(œ): however, one must remember that the «-component spectrum is the frequency distribution of contributions to u2, not yju2. 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.

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