Abstract

Self-similarity is a symmetry appearing in many problems of mechanics. If present, it allows for a simplification of the governing partial differential equations, leading to a better understanding of the underlying physical processes. When considering turbulent flows in particular, it is at the core of many well-known theoretical results (e.g., law of the wall, power-law evolution of free shear flows). In this talk I will discuss some recent findings: First, I will show that the assumption of a self-similar cascade in homogenous turbulence can lead to a large-scale correction to Kolmogorov’s -5/3 law. Second, I will discuss the conditions of appearance of self-similarity in turbulent shear flows; recent results suggest that Townsend’s proposition, attributing the onset of self-similarity to the disappearance of the memory of initial conditions, might not be fully accurate. Third, I will present a novel data-driven methodology that allows the extraction of self-similar dynamics directly from data, without prior knowledge of the flow physics, nor of the underlying governing equations.