Self-attenuation of extreme events in Navier–Stokes turbulence

Dhawal Buaria (), Alain Pumir and Eberhard Bodenschatz
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Dhawal Buaria: Max Planck Institute for Dynamics and Self-Organization
Alain Pumir: Max Planck Institute for Dynamics and Self-Organization
Eberhard Bodenschatz: Max Planck Institute for Dynamics and Self-Organization

Nature Communications, 2020, vol. 11, issue 1, 1-7

Abstract: Abstract Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations. A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of Navier-Stokes equations, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and even establishing regularity of the equations. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to Navier-Stokes equations, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of Navier-Stokes equations.

Date: 2020
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DOI: 10.1038/s41467-020-19530-1

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