Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes

Abstract

Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_1,l_2,l)$ and $B(l,l_1,l_2)$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_1$and $l_2$ collide and form the single loop of length $l=l_1+l_2$. Quantity describes the rate of events, when the single loop of the length $l$ breaks down into two the daughter loops of lengths $l_1$ and $l_2$. These quantities ave evaluated as the averaged numbers of zeroes of vector $\mathbf{S}$ connecting two points on the loops of ${\xi }_2$ and ${\xi }_1$ at moment of time $t$. Statistics of the individual loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40

9 pages, 5 figures, To be submitted to JLTP

Cited by in corpus (4)

• Bottleneck crossover between classical and quantum superfluid turbulence
• Diffusion of Inhomogeneous Vortex Tangle and Decay of Superfluid Turbulence
• Kinetics of a Network of Vortex Loops in He II and a Theory of Superfluid Turbulence
• Evolution of a Network of Vortex Loops in the Turbulent Superfluid Helium; Derivation of the Vinen Equation