Johan Hoffman: Turbulence as the stability of three fundamental flow structures

Abstract: In this talk we present a model of turbulence based on the stability of three fundamental flow structures. Any flow field can be decomposed into a sum of the three flow structures: rigid body rotational flow, straining flow, and shear flow. This triple decomposition is based on the standardized real Schur form of the velocity gradient tensor. The Navier-Stokes equations are then used to assign to each flow structure a local stability property based on the rate of perturbation growth in turbulent flow (at scales larger than the smallest microscales which are dominated by viscosity): rigid body rotational flow is stable, shear flow is linearly (or quadratically) unstable, and straining flow is exponentially unstable; which implies that rotational flow (vortices) can exits for a long time, shear flow for a short time, and straining flow only for a very short time. We present this model in an accessible way to non-experts, and we use the model to propose a new physical mechanism for turbulence generation and inverse energy transfer.