Abstract
The nonlinear and nonlocal coupling of vorticity and strain rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly resolved direct numerical simulations of isotropic turbulence in periodic domains of up to 122883 grid points and Taylor-scale Reynolds number Rλ in the range 140–1300, we investigate this nonlocality by decomposing the strain-rate tensor into local and nonlocal contributions obtained through Biot-Savart integration of vorticity in a sphere of radius R. We find that vorticity is predominantly amplified by the nonlocal strain coming beyond a characteristic scale size, which varies as a simple power law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of nonlocal strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power law and ultimately also the scale invariance of vorticity amplification, with important implications for prevailing intermittency theories.Received 13 May 2021Accepted 19 October 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042020Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGeophysical fluid dynamicsTurbulenceTechniquesComputational complexityExtreme event statisticsLarge deviation & rare event statisticsNavier-Stokes equationFluid DynamicsNonlinear DynamicsStatistical Physics
Highlights
Complex nonlinear physical systems are often characterized by formation of extreme events, which strongly deviate from Gaussianity, necessitating anomalous corrections to mean-field descriptions [1,2,3]
The canonical description based on angular momentum conservation dictates that as vortical filaments are stretched by strain, they become thinner and spin more quickly, enabling gradient amplification and simultaneously driving the energy cascade from large to small scales [8,9]
In this Letter, we investigate the nonlocality of vorticity self-amplification by tackling the Biot-Savart integral in Eq (2) via direct numerical simulations (DNS) of incompressible Navier-Stokes equations (INSE) [6]
Summary
Fluid turbulence, described by the three-dimensional incompressible Navier-Stokes equations (INSE), is an emblematic example of such a system, where extreme events are associated with intermittent formation of large velocity gradients, organized into thin filaments of intense vortices [4,5,6,7]. The amplification of such intense gradients is readily described by the vortex-stretching mechanism, which expresses the nonlinear stretching of vorticity ω, by the strain-rate tensor Si j in the INSE (written as the vorticity equation)
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