5 research outputs found
Geometry of turbulent dissipation and the Navier-Stokes regularity problem
The question of whether a singularity can form in an initially regular flow,
described by the 3D incompressible Navier-Stokes (NS) equations, is a
fundamental problem in mathematical physics. The NS regularity problem is
super-critical, i.e., there is a 'scaling gap' between what can be established
by mathematical analysis and what is needed to rule out a singularity. A
recently introduced mathematical framework--based on a suitably defined `scale
of sparseness' of the regions of intense vorticity--brought the first scaling
reduction of the NS super-criticality since the 1960s. Here, we put this
framework to the first numerical test using a spatially highly resolved
computational simulation performed near a 'burst' of the vorticity magnitude.
The results confirm that the scale is well suited to detect the onset of
dissipation and provide strong numerical evidence that ongoing mathematical
efforts may succeed in closing the scaling gap.Comment: 9 pages, 4 figure