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Twisting vortex lines regularize Navier-Stokes turbulence
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DOI：10.1126/sciadv.ado1969.png)
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摘要
En 中文
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.
Keyword:
POTENTIALLY SINGULAR SOLUTIONS
ISOTROPIC TURBULENCE
EULER EQUATIONS
VORTICITY
DYNAMICS
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期刊
IF:
12.5
论文数:
2.1W
被引数:
18.1W
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Spontaneous symmetry breaking for extreme vorticity and strain in the three-dimensional Navier-Stokes equations.png)
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