I will begin with presenting and illustrating the standard phenomenology of three-dimensional (statistically) isotropic and homogeneous fluid turbulence, which is mainly attributed to Kolmogorov. Then, while designing random fields able to reproduce/model the implied intricate spatial structure of kinematic quantities of interest, and some crucial mechanisms of the Navier-Stokes equations, I will explain how come the celebrated Harish-Chandra–Itzykson–Zuber integral over the orthogonal group enters in a probabilistic picture of such a phenomenology. This aspect has been developed with C. Garban, R. Pereira, R. Rhodes, R. Robert and V. Vargas. [The talk will be streamed online, please ask the organizers for the link.]

Laboratoire de physique, CNRS/ENS de Lyon