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

Anomalous dissipation is a mechanism to dissipate 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>Re</a:mi></a:math>, the dimensionless parameter that characterizes the strength of turbulence, given that <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>Re</b:mi><b:mo>≫</b:mo><b:mn>1</b:mn></b:mrow></b:math>. The present study aims at bridging this statistical behavior of high-Reynolds-number turbulence to one specific structural building block of fluid turbulence—local vortex stretching configurations which take in the simplest case the form of Burgers's 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 analyze 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 correspond to precursors of enhanced anomalous dissipation. Published by the American Physical Society 2024