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On quantum turbulence in superfluid 4He

Lipniacki T.

Archives of Mechanics

2001

Vol. 53, nr 1

23-43

The alternative approach to the homogeneous quantum turbulence is proposed in order to derive the evolution equation for vortex line-length density. Special attention is paid to reconnections of vortex lines. According to our previous paper, the summary line-length change delta s of two vortex lines resulting from the reconnection (in the presence of counterflow Vns) can be approximated by the expression: .... The dynamics of vortex lines in the tangle is considered as a sequence of reconnections followed by "free" evolutions. For the steady-state turbulence, the average line-length change between reconnections has to be zero. If, for a given value of the counterflow, the line density is smaller than the equilibrium one, the reconnections occur less frequently and becomes positive. As a result, the line density grows until the equilibrium is restored. On the other hand, when the line-density is too large, the reconnections are very frequent, so the lines shorten between reconnections and the line density becomes smaller. The time derivative of total line density is proportional to the reconnection frequency multiplied by the average line-length change due to a single reconnection. The evolution equation obtained in the proposed approach resembles the alternative Vinen equation.

Dynamics of quantum vortices in superfluid '4He

Lipniacki T.

Archives of Mechanics

1998

Vol. 50, nr 3

467-482

The dissipative motion of quatized vortex line, after reconnection, is studied within the localized induction approximation. The numerical symulations of vortex line evolution help to determine the rate of the line-length changes. In the absence of counterflow, the vortex line shortens after each reconnection and line-length reduction is calculated as a function of friction parametr alpha and reconnection angle phi. The obtained results sugest that the decay of quantized vortex tangle is due to line-length reduction which occurs after each reconnection of vortex lines. In the presence of the counterflow, however, the reconnection may initiate a generation of a cascade of vortex loops. These loops blow up, so the totallength of vortices grows up and the quantum turbulece can be generated.