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7 Renormalized Perturbation Theories of the Second Kind
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Published:July 1990
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Abstract
In the preceding chapter, we discussed the pioneering theories of turbulence, in which systematic renormalization methods were introduced to the subject for the first time, but we did not dwell to any extent on the virtues (or otherwise) of these theories. We shall continue to defer such considerations, for the most part, to Chapter 8, where the overall assessment of RPTs will be considered in some detail. However, before turning our attention to those theories which do yield the Kolmogorov spectrum as a solution, we shall make a rather limited analysis of certain unsatisfactory features of the older theories. Our reason for doing this at the present stage, is that it provides a perspective into which we can fit the development of the newer theories. Inevitably this means that the discussion is conducted in terms of failures to achieve the Kolmogorov form of the energy spectrum. Nevertheless, this should not be taken to mean that we are asserting that the Kolmogorov distribution provides a crucial test for analytic turbulence theories.
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