Investigation of the viscous reconnection phenomenon of two vortex tubes through spectral simulations

This paper aims to shed further light on the viscous reconnection phenomenon. To this end, we propose a robust and efficient method in order to quantify the degree of reconnection of two vortex tubes. This method is used to compare the evolutions of two simple initial vortex configurations: orthogonal and antiparallel. For the antiparallel configuration, the proposed method is compared with alternative estimators and it is found to improve accuracy since it can account properly for the formation of looping structures inside the domain. This observation being new, the physical mechanism for the formation of those looping structures is discussed. For the orthogonal configuration, we report results from simulations that were performed at a much higher vortex Reynolds number (Re-Gamma = circulation/ viscosity = 10(4)) and finer resolution (N-3 = 1024(3)) than previously presented in the literature. The incompressible Navier-stokes equations are solved directly (Direct Numerical Simulation or DNS) using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The associated zero-circulation constraint is circumvented by solving the governing equations in a proper rotating frame of reference. Using ideas similar to those behind our method to compute the degree of reconnection, we split the vorticity field into its reconnected and non-reconnected parts, which allows to create insightful visualizations of the evolving vortex topology. It also allows to detect regions in the vorticity field that are neither reconnected nor non-reconnected and thus must be associated to internal looping structures. Finally, the Reynolds number dependence of the reconnection time scale T-rec is investigated in the range 500 <= Re-Gamma <= 10 000. For both initial configurations, the scaling is generally found to vary continuously as Re-Gamma is increased from T-rec similar to Re-Gamma(-1) to T-rec similar to Re-Gamma(-1/2), thus providing quantitative support for previous claims that the reconnection physics of two vortices should be similar regardless of their spatial arrangement. Published by AIP Publishing.