“Turbulence, shell models and critical exponents for dissipation”
Martedì 18 Febbraio 2020, ore 10:30 - Aula 2BC30 - Francesco Morandin
Shell models of turbulence are nonlinear dynamical systems inspired by fluid dynamics. They are idealized and simplified, but tailored to exhibit the same energy cascade behaviour of three dimensional Euler and Navier-Stokes equations. A typical feature of these models is in fact anomalous dissipation of energy, which in finite time “escapes” to infinity, yielding a blow-up and instantaneous loss in regularity. A dissipative term corresponding to viscosity can recover regularity, for some of these models, but in total generality one needs hyper-dissipation, with an exponent larger than the physical one. Recent results hint that in the more refined framework of tree (hierarchical) models the required exponent may be actually lower.