Abstract:
The celebrated (homogeneous and isotropic) Kolmogorov’s Theory of Turbulence from 1941 empirically fails because of space-time concentration of singular structures. This phenomenon is known as “intermittency”. I will show how intermittency can be rigorously measured/proved by studying the possible lower-dimensional accumulation of energy dissipation. Different notions of dimensionality lead to different conclusions, each of them capturing some relevant aspects of turbulent flows. I will keep the presentation quite general and conceptual, giving a few proofs of easy toy models which might also have an independent interest.