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Self-attenuation of extreme events in Navier–Stokes turbulence

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 deformationrate (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.
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https://hal.archives-ouvertes.fr/hal-03010637
Contributor : Alain Pumir <>
Submitted on : Monday, November 30, 2020 - 4:12:42 PM
Last modification on : Monday, November 30, 2020 - 4:21:02 PM

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Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz. Self-attenuation of extreme events in Navier–Stokes turbulence. Nature Communications, Nature Publishing Group, 2020, 11 (1), ⟨10.1038/s41467-020-19530-1⟩. ⟨hal-03010637⟩

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