Boundary conditions and vortex wandering

A direct numerical simulation of a Batchelor vortex has been carried out in the presence of freely decaying turbulence, using both periodic and symmetric boundary conditions; the latter most closely approximates typical experimental conditions, while the former is often used in computational simulations for numerical convenience. The higher-order velocity statistics were shown to be strongly dependent upon the boundary conditions, but the dependence could be mostly eliminated by correcting for the random, Gaussian modulation of the vortex trajectory, commonly referred to as ‘wandering’, using a technique often employed in the analysis of experimental data. Once this wandering had been corrected for, the strong peaks in the Reynolds stresses normally observed at the vortex centre were replaced by smaller local extrema located within the core region but away from the centre. The distributions of the corrected Reynolds stresses suggest that the formation and organization of secondary structures within the core is the main mechanism in turbulent production during the linear growth phase of vortex development.