Analysis of Reynolds number scaling for viscous vortex reconnection

Abstract

A theoretical analysis of viscous vortex reconnection is developed based on scale separation, and the Reynolds number, Re (= circulation/viscosity), scaling for the reconnection time Trec is derived. The scaling varies continuously as Re increases from Trec ~Re-Trec ~Re. This theoretical prediction agrees well with direct numerical simulations by Garten et al. [J. Fluid Mech.426, 1 (2001)]10.1017/S0022112000002251 and Hussain and Duraisamy [Phys. Fluids23, 021701 (2011)]10.1063/1.3532039. Moreover, our analysis yields two Re's, namely, a characteristic Re Re0.75 ε[o(103O(103)for the Trec Re0.75scaling given by Hussain and Duraisamy and the critical Re RecO(104) for the transition after which the first reconnection is completed. For >, a quiescent state follows, and then, a second reconnection may occur. © 2012 American Institute of Physics.