Abstract
Turbulent pipe flow is commonly described in terms of a law of the wall and a law of the wake, which match with one another in a region of overlap. This suggests that the flow ought to be analyzed with singular perturbation methods; the main features of an approach based on these methods are explored in this paper. The crucial part of the analysis is the second-order flow in the wall layer. Because of the lack of other reliable information, the equation governing second-order effects in the wall layer is solved by analogy with the firstorder flow in the wall layer of boundary layers with zero wall stress. Taking the secondorder solution into account, the slope of the logarithmic velocity profile is 2.95-4.4R+~, where /?_}_ = ruT/v and r is the pipe radius. A friction law with second-order corrections is also presented.
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