Intermittency, cascades and thin sets in threedimensional NavierStokes turbulence
Abstract
Visual manifestations of intermittency in computations of threedimensional NavierStokes fluid turbulence appear as the lowdimensional or "thin" filamentary sets on which vorticity and strain accumulate as energy cascades down to small scales. In order to study this phenomenon, the first task of this paper is to investigate how weak solutions of the NavierStokes equations can be associated with a cascade and, as a consequence, with an infinite sequence of inverse length scales. It turns out that this sequence converges to a finite limit. The second task is to show how these results scale with integer dimension $D=1, 2, 3$ and, in the light of the occurrence of thin sets, to discuss the mechanism of how the fluid might find the smoothest, most dissipative class of solutions rather than the most singular.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 September 2020
 DOI:
 10.1209/02955075/131/64001
 arXiv:
 arXiv:2009.01556
 Bibcode:
 2020EL....13164001G
 Keywords:

 47.27.Gs;
 47.53.+n;
 47.10.ad;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 1 figure containing 2 subfigures