Slow Transient Processes in the Second Sound Resonator

TL;DR

This paper develops a multi-scale perturbation method to isolate slow hydrodynamic processes in superfluid helium, enabling accurate analysis of unsteady heat transfer and vortex dynamics in second sound resonators.

Contribution

The authors introduce a novel multi-scale perturbation approach to eliminate fast sound processes, deriving equations that describe the slow evolution of vortex line density and heat transfer in HeII.

Findings

Long-term heat load evolution follows nonlinear heat conductivity.

Correct vortex line density dynamics can be extracted from second sound measurements.

The method improves interpretation of nonstationary vortex behavior in resonators.

Abstract

The Hydrodynamics of Superfluid Turbulence (HST) describes the flows (or counterflows) of HeII in the presence of a chaotic set of vortex filaments. The HST equations govern both a slow variation of the hydrodynamic variables due to dissipation related to the vortex tangle and fast processes of the first and second sound propagation. This circumstance prevents effective numerical simulations of the problems of unsteady heat transfer in HeII. By virtue of a pertinent multi-scale perturbation analysis we show how one can eliminate the fast processes to derive the evolution equation for the slow processes only. We then demonstrate that the long-term evolution of a transient heat load of moderate intensity obeys the nonlinear heat conductivity equation. The second example of the methods developed is investigation of unsteady processes in the second sound resonator. The latter is frequently used for study of nonstationary behavior of vortex tangle, just by monitoring of the quality factor behavior. This procedure however is wrong when characteristic times of processes are comparable (or smaller) than the time constant of resonator. We show how to extract the correct information on the vortex line density (VLD) dynamics with use of procedure we developed. PACS numbers: 47.32.Cc, 47.37.+q, 67.40.Vs., 05.10.Gg.