Eddy-Viscous Modeling and the Topology of Extreme Circulation Events in Three-Dimensional Turbulence

TL;DR

This paper explores the structure and evolution of extreme turbulent circulation events in 3D turbulence using instanton theory, revealing a surprising vortex ring topology and combining phenomenological and numerical methods.

Contribution

It introduces a novel numerical approach to solve axisymmetric instanton equations and uncovers the topological structure of circulation instantons in turbulence.

Findings

Instantons model the core of extreme circulation events effectively.

Circulation instantons form paired counter-rotating vortex rings.

The approach highlights limitations in describing the tails of instanton distributions.

Abstract

We discuss the role of particular velocity field configurations -- instantons, for short -- which are supposed to dominate the flow during the occurrence of extreme turbulent circulation events. Instanton equations, devised for the stochastic hydrodynamic setup of homogeneous and isotropic turbulence, are applied to the interpretation of direct numerical simulation results. We are able in this way to model the time evolution of extreme circulation events for a broad range of scales, through the combined use of eddy viscosity phenomenology and exact creeping instantons. While this approach works well for the core of circulation instantons, it fails to describe their tails. In order to overcome this difficulty, we put forward a numerical treatment of the axisymmetric instanton equations. Circulation instantons are then found to have a surprising topological structure, which consists of a system of paired counter-rotating vortex rings centered around the symmetry axis of a background axisymmetric vortical flow.