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arXiv · 2009.08370

Self-attenuation of extreme events in Navier-Stokes turbulence

Dhawal Buaria·Alain Pumir·Eberhard Bodenschatz
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Abstract

Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations (INSE). 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 INSE, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and in establishing regularity of INSE. 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 INSE, 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 INSE.

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Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz. 2020-09-17. Self-attenuation of extreme events in Navier-Stokes turbulence. https://doi.org/10.1038/s41467-020-19530-1

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