Shell model of superfluid turbulence

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.

25 pages, 14 figures, to be published in PRB

References in corpus (5)

• Turbulent velocity spectra in superfluid flows
• Spectrum of turbulent Kelvin-waves cascade in superfluid helium
• Energy Spectra of Developed Turbulencein Helium Superfluids
• Mesoscale Equipartition of kinetic energy in Quantum Turbulence
• Vortex density fluctuations in quantum turbulence

Cited by in corpus (13)

• Cascades and transitions in turbulent flows
• Introduction to quantum turbulence
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Enhancement of intermittency in superfluid turbulence
• Variable energy flux in turbulence
• Quantitative estimation of effective viscosity in quantum turbulence
• Multiscaling in superfluid turbulence: A shell-model study
• Energy Spectra of Superfluid Turbulence in ${}^3$He
• Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model
• Finite temperature effects in helical quantum turbulence
• The Statistical Properties of Superfluid Turbulence in ${}^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model
• Statistics of Quantum Turbulence in Superfluid He
• Dynamic Scaling in Rotating Turbulence: A Shell Model Study