SELF-SIMILAR SPIRAL FLOW STRUCTURE IN LOW-REYNOLDS-NUMBER ISOTROPIC AND DECAYING TURBULENCE

It is rigorously proved for axisymmetric incompressible flows with bou nded axial vorticity at infinity that if a spiral-helical streamline h as a Kolmogorov capacity (box-counting dimension) D-K>1 then the veloc ity field must have a singularity at the axis of symmetry. Furthermore , certain types of singularity with D-K=1 can be excluded. The Burgers and the Lundgren vortices are examples of strained vortices with diff erent types of near-singular structure, and in both cases sections of streamlines have a well-defined D-K>1. However, the strain severely li mits the region in space where D-K is larger than 1. An algorithm is d eveloped which detects streamlines with persistently strong curvature and calculates both the D-K of the streamlines and the lower bound sca le delta(min) of the range of self-similar scaling defined by D-K. Err or bounds on D-K are also computed. The use of this algorithm partly r elies on the fact that two to three turns of a spiral are enough to de termine a spiral's D-K. We detect well-defined self-similar scaling in the geometry of streamlines around vortex tubes in decaying isotropic direct numerical simulation turbulence with exceptionally fine small- scale resolution and Re-lambda around 20. The measured values of D-K v ary from D-K=1 to D-K approximate to 1.60, and in general the self-sim ilar range of length scales over which D-K is well defined extends ove r one decade and ends at one of two well-defined inner scales, one jus t above and the other just below the Kolmogorov microscale eta. We ide ntify two different types of accumulation of length scales with D-K>1 on streamlines around the vortex tubes in the simulated turbulence: an accumulation of the streamline towards a central axis of the vortex t ube in a spiral-helical fashion, and a helical and axial accumulation of the streamline towards a limit circle at the periphery of the vorte x tube. In the latter case, the limit circle lies in a region along th e axis of the vortex tube where there is a rapid drop in enstrophy. Th e existence of spiral-helical streamlines with well-defined D-K>1 sugg ests the possibility of a near-singular flow structure ih some vortex tubes. Finally, we present some evidence based on the spatial correlat ion of enstrophy with viscous force indicating that the spatial vortic ity profile across vortex tubes is not a well-resolved Gaussian at the resolution of the present simulations.