Turbulence: Statistical Approach

The statistics of velocity differences in turbulence gives an example of both the limitations of scale invariance and the generic character of the corrections it implies. In this lecture, as an introduction I shall present another case where such limitations appear, by successive refinements of a dimensional analysis approach: the turbulent velocity profile close to the wall of a channel. Then I shall discuss the velocity intermittency phenomenon in homogeneous, isotropic turbulent flows. I shall finish with a new Markovian approach for this problem, mainly stressing the connection with the previous one.

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