Friday April 23rd, 2021 | |
| Time: | 2:30 PM - 3:30 PM |
| Title: | Statistical conservation laws, scaling and renormalisation in the Kraichnan model of passive advection. |
| Speaker: | Paolo Muratore-Ginanneschi, University of Helsinki |
| Abstract: | |
| A complete understanding of the link between the dynamics and the statistics of indicators of a turbulent Newtonian fluid remains a grand open challenge in theoretical and mathematical physics. In particular, a theory predicting in a mathematically controlled fashion experimentally and numerically observed scaling properties of indicators of the flow is still missing. During the last decade of last century and the first decade of the present one, the study of the Kraichnan model of passive advection made possible to obtain a mathematically controlled derivation of multiscaling for the first time in turbulence theory. The proof of multiscaling highlighted the existence of a general relation between the statistical conservation laws satisfied by Lagrangian particle shapes contributing to the correlation functions and the occurrence anomalous scaling. In the inertial range the statistically conserved structures can be also described as composite operators perturbing a scaling fixed point of a Wilsonian renormalization map. In my talk I will give an overview on these developments with emphasis on how renormalization group ideas have been applied in the context of studying intermittency in the Kraichnan model. | |