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.
Highlights
Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations
It has been proven that this unbounded growth can possibly only occur when the viscosity ν is sufficiently small[4], which would correspond to turbulent solutions of the incompressible Navier–Stokes equations (INSE)
To analyze the complex interaction between strain and vorticity, we utilize our unique database generated through direct numerical simulations (DNS) of the INSE
Summary
For intense value shown, negative stretching rate is more prevalent especially around the center where vorticity is maximum We note that the values of PLΩ are overwhelmingly negative for large Ω, as corroborated by the observation (not shown in figure) that conditional expectations of jPLΩj and j À PLΩj are virtually equal. This reaffirms that PLΩ is predominantly negative when conditioned on large values of Ω, and consolidates the observed selfattenuation mechanism. In fully developed turbulence, the intense whirling motions (vortex tubes), emblematic of the small-scale structures, are innately three-dimensional and helical
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
