Abstract
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. A recently developed numerical method, based on compact schemes combined with three stage Runge-Kutta method for time integration, with projection method for enforcing continuity is used for numerical simulations. The Poisson solver used is a direct solver in spectral space. 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. Analysis of the budgets of turbulent kinetic energy and normal Reynolds stress suggest that the production budget during the growth phase of vortex development, resembles turbulent boundary layer type budgets. The analysis of the budgets of turbulent shear stresses shows that the formation and organization of `hairpin' (secondary) structures within the core is the main mechanism for turbulent production and the budget of TKE and radial tangential shear stress shows a turbulent boundary layer type budget.