Vortex Stretching in Vortex Reconnection

In this study, we dealt with a rapid and explosive vortex stretching in vortex reconnection of two vortex rings, and aimed to estimate the speed of vortex stretching and to provide considerations to it from the perspectives of thermodynamics, statistical mechanics and control engineering. As a method, both of Biot-Savart simulation and Navier-Stokes simulation were used. Firstly, from the temporal changes in the stretching rate, the logarithm of stretching rate and the exponent of exponential increase of stretching rate, the speed of vortex stretching was estimated quantitatively. Then, in the temporal change in the logarithm of stretching rate, a transition point was observed near the reconnection occurrence time, and at the transition point, the speed of vortex stretching changed significantly. Secondly, several considerations were given to such results from the perspectives of the entropy in thermodynamics and statistical mechanics and of the Lyapunov exponent in control engineering.