Local precursors to anomalous dissipation in Navier-Stokes turbulence: Burgers vortex-type models and simulation analysis

TL;DR

This paper investigates the connection between local vortex stretching structures, modeled by Burgers vortices, and anomalous energy dissipation in high-Reynolds-number turbulence through analytical models and numerical simulations.

Contribution

It bridges the statistical phenomenon of anomalous dissipation with specific local vortex structures using analytical models and turbulence simulation data.

Findings

High-vorticity events resemble Burgers vortex models

Local vortex stretching precursors to anomalous dissipation identified

Analysis links vortex structures to energy dissipation mechanisms

Abstract

Anomalous dissipation is a dissipation mechanism of kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to Reynolds number ${\rm Re}$, the dimensionless parameter that characterizes the strength of turbulence, given that ${\rm Re}\gg 1$. The present study aims at bridging this statistical behavior of high-Reynolds-number turbulence to specific structural building blocks of fluid turbulence -- local vortex stretching configurations which take in the simplest case the form of Burgers' classical vortex stretching model from 1948. We discuss the anomalous dissipation in the framework of Duchon and Robert for this analytical solution of the Navier-Stokes equations, apply the same analysis subsequently to a generalized model of randomly oriented Burgers vortices by Kambe and Hatakeyama, and analyse finally direct numerical simulation data of three-dimensional homogeneous, isotropic box turbulence in this respect. We identify local high-vorticity events in fully developed Navier-Stokes turbulence that approximate the analytical models of strong vortex stretching well. They also correspond to precursors of enhanced anomalous dissipation.