Integration of slow-fast quasilinear models of turbulent shear flows

by Dr Alessia Ferraro (EPFL)

Monday 14 Nov 2022, 15:45 → 16:45 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

zoom link : https://stockholmuniversity.zoom.us/j/622224375

The quasilinear (QL) reduction, which retains fluctuation-fluctuation nonlinearities only where they feed back onto mean fields, is often employed as a model reduction strategy. This approximation can be justified in the limit of temporal scale separation between the mean and fluctuation dynamics as arises, e.g., in the asymptotic description of strongly stratified shear turbulence and of exact coherent states in wall-bounded shear flows. A recently introduced mathematical formalism for the integration of slow-fast QL systems exploits the tendency of these systems to self-organize about a marginal stability manifold and slaves the amplitude of the (marginal) fluctuations to the slowly-evolving mean field. Here, we utilise carefully constructed model problems to derive two important extensions to this formalism. The first extension accommodates large-amplitude bursting events, in which temporal scale separation is transiently lost, requiring the co-evolutions of the slow and the fast fields on the same temporal scale until marginal stability is re-established. The second extension yields a slow evolution equation for the wavenumber of the fastest growing mode, whose amplitude is then slaved to the mean field dynamics in condition of marginal stability to maintain a zero growth rate. Together, these extensions enable scale-selective adaptivity in both space and time. Our formalism is consistent with the idea that shear flow turbulence tracks low-dimensional state space structures (marginally stable manifolds) during slow evolutionary phases punctuated by intermittent bursting events.