2020/09/17 by Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz · 59 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Compressibility #Fluid Dynamics and Turbulent Flows #Fluid dynamics and aerodynamics studies #Mechanism (biology) #Navier-Stokes equation solutions #RADIUS #State (computer science) #Turbulence #Vortex #Vorticity #Vorticity equation #cs.NA #math.NA #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.1038/s41467-020-19530-1
published in Nature Communications 11(1), 5852 (Nature Portfolio) · 8 pages, 3 figures
arxiv created 2020/09/17 · openalex created_date 2020/09/21 · openalex publication_date 2020/11/17 · arxiv updated 2020/11/18 · openalex updated_date 2026/08/05
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.