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2 The Fundamental Approach
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Published:July 1990
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Abstract
Superficially the background material presented in this chapter may seem very similar to the topics covered in Chapter 1. That is, we begin with the Navier-Stokes equations and use the Reynolds averaging procedure to formulate the statistical approach. Then (just as in Chapter 1) we are concerned with the mean square excitation of fluctuations, with energy balances, and with the moment closure problem. We shall also consider the use of both dimensional methods and approximate models, and conclude by considering some representative experimental results. However, there will be two important differences of emphasis. First of all, our main interest will be in the underlying structure of the turbulence. That is, we shall consider the correlation of velocities at two or more points (and times). The foundations of this approach were laid by Taylor (1935) in a paper which also introduced the concepts of statistical homogeneity and isotropy: a step which took turbulence theory into the realm of physics, rather than engineering. In a subsequent paper (Taylor 1938a) the introduction of the energy spectrum in wavenumber (i.e. the Fourier transform of the two-point correlation in space) virtually completed this process, and, as we shall see, the calculation of this spectrum provides a major goal for fundamental turbulence theory.
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