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Logarithmic profile of the mean turbulent velocity and recent developments about its universality.

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TUR - Mathematical aspects of turbulence: where do we stand?

When I introduce turbulent flow to my engineering students I begin by the statement that there are properties of it that, at the present state of knowledge, we just can’t predict, and properties that, despite the lack of a complete mathematical model, we can predict with a few percent accuracy. An example of the last category is the mean velocity profile between parallel plane walls or in a pipe which, in analogy to the Kolmogorov spectrum of homogeneous turbulence, can be predicted by dimensional analysis coupled with a judicious conjecture of what are the relevant physical quantities. Introduced a century ago by Prandtl and perfected by many others, this is one of the mainstays of the theory and practice of fully developed turbulence, yet its details have been under scrutiny until very recently and this presentation will show some unexpected twists.

This talk is part of the Isaac Newton Institute Seminar Series series.

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