The problem of evolution of strong heat pulses in He II interacting with quantum vortices induced by these pulses is investigated numerically on the basis of equations of hydrodynamics of superfluid turbulence. In order to study nonlinear effects, the initial equations are expanded to the second order in the amplitudes of pulses. The one-dimensional case in the absence of mass transport (second sound) is considered. The initiation of vortices was simulated by the generation term in the Vinen equation. The results on the dynamics of pulses in various temperature ranges are presented. It is shown that the Feynman–Vinen theory is applicable in the phase-transition region.
We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the interaction with the normal component, or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, e.i. we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-disspation relation, which implies that thermodynamic equilibrium should be reached. In the paper we describe the numerical methods for integration of stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of calculation of some characteristics of a vortex tangle such as the total length, distribution of loops in the space of their length, and the energy spectrum.
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