Shell model of superfluid turbulence

TL;DR

This paper introduces a two-fluid shell model to analyze superfluid helium turbulence, examining energy spectra, flux balances, and deviations from classical turbulence spectra across temperatures.

Contribution

It presents a novel two-fluid shell model for superfluid turbulence, capturing energy transfer and spectral deviations due to mutual friction.

Findings

Energy accumulates at high wavenumbers at low temperatures

Mutual friction causes deviations from the classical $k^{-5/3}$ spectrum

Results align with experimental observations and suggest additional dissipation mechanisms

Abstract

Superfluid helium consists of two inter-penetrating fluids, a viscous normal fluid and an inviscid superfluid, coupled by a mutual friction. We develop a two-fluid shell model to study superfluid turbulence. We investigate the energy spectra and the balance of fluxes between the two fluids as a function of temperature in continuously forced turbulence, and, in the absence of forcing, the decay of turbulence. We furthermore investigate deviations from the $k^{-5/3}$ spectrum caused by the mutual friction force. We compare our results with experiments and existing calculations. We find that, at sufficiently low temperatures a build-up of energy develops at high wavenumbers suggesting the need for a further dissipative effect, such as the Kelvin wave cascade and phonon emission.