Twisting vortex lines regularize Navier-Stokes turbulence

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Buaria, Dhawal ; Lawson, John M. ; Wilczek, Michael:
Twisting vortex lines regularize Navier-Stokes turbulence.
In: Science Advances. Bd. 10 (2024) Heft 37 . - eado1969.
ISSN 2375-2548
DOI: https://doi.org/10.1126/sciadv.ado1969

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Abstract

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders spontaneous self-stretching and twisting of vortex lines, generating a complex hierarchy of structures. While the INSE are routinely used to describe turbulence, their regularity remains unproven; the implicit assumption being that the self-stretching is ultimately regularized by viscosity, preventing any singularities. Here, we uncover an inviscid regularizing mechanism stemming from self-stretching itself, by analyzing the flow topology as perceived by an observer aligned with the vorticity vector undergoing amplification. While, initially, vorticity amplification occurs via increasing twisting of vortex lines, a regularizing anti-twist spontaneously emerges to prevent unbounded growth. By isolating a vortex, we additionally demonstrate the genericity of this self-regularizing anti-twist. Our work, directly linking dynamics of vortices to turbulence statistics, reveals how the Navier-Stokes dynamics avoids the development of singularities even without the aid of viscosity. Analysis of how vortex lines twist in turbulent flows identifies the physical mechanism underpinning Navier-Stokes regularity.