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Reconnection plays a significant role in the dynamics of plasmas, polymersand macromolecules, as well as in numerous laminar and turbulent flow phenomenain both classical and quantum fluids. Extensive studies in quantum vortexreconnection show that the minimum separation distance {\delta} betweeninteracting vortices follows a 1/2 scaling. Due to the complex nature of thedynamics (e.g., the formation of bridges and threads as well as successivereconnections and avalanche), such scaling has never been reported for(classical) viscous vortex reconnection. Using the direct numerical simulationof the Navier-Stokes equations, we study viscous reconnection of slendervortices, whose core size is much smaller than the radius of the vortexcurvature. For separations that are large compared to the vortex core size, wediscover that {\delta}(t) between the two interacting viscous vorticessurprisingly also follows the 1/2 power scaling for both pre- andpost-reconnection events. The prefactors in this 1/2-power law are found todepend not only on the initial configuration but also on the vortex Reynoldsnumber (or viscosity). Our finding in the viscous reconnection, complementingnumerous works on quantum vortex reconnection, suggests that there is indeed auniversal route for reconnection -- an essential result for understanding thevarious facets of the viscous vortex reconnection phenomena and their potentialmodeling, as well as possibly explaining turbulence cascade physics.

Separation scaling for viscous vortex reconnection