Self-attenuation of extreme events in Navier-Stokes turbulence

TL;DR

This paper reveals a self-attenuation mechanism in turbulence where local strain counteracts vorticity amplification, potentially aiding in proving the regularity of the Navier-Stokes equations.

Contribution

It introduces a novel separation of strain into local and non-local parts, uncovering how local strain suppresses extreme vorticity growth in turbulent flows.

Findings

Local strain counteracts vorticity amplification at high vorticity levels

Self-attenuation linked to local Beltramization of flow

Potential implications for Navier-Stokes regularity proof

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.