Mesoscale Equipartition of kinetic energy in Quantum Turbulence

Abstract

The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vortex spacing varies with the Reynolds number as $R{e}^{-3/4}$, like the viscous length scale in classical turbulence. In the high temperature limit, Kolmogorov's inertial cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the inertial cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes, with a characteristic $k^2$ velocity spectrum. The accumulation of superfluid excitations on a range of mesoscales enables the superfluid to keep dissipating kinetic energy through mutual friction with the residual normal fluid, although the later becomes rare at low temperature. It is found that most of the superfluid vorticity can concentrate on these mesoscales at low temperature, while it is concentrated in the inertial range at higher temperature. This observation should have consequences on the interpretation of decaying turbulence experiments, which are often based on vortex line density measurements.

6 pages, 5 figures

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Cited by in corpus (13)

• Introduction to quantum turbulence
• Energy cascade and the four-fifths law in superfluid turbulence
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• Intermittency of quantum turbulence with superfluid fractions from 0% to 96%
• Vortex density fluctuations in quantum turbulence
• Detection of vortex coherent structures in superfluid turbulence
• On the investigation of properties of superfluid ${}^4$He turbulence using a hot-wire signal
• Local measurement of vortex statistics in quantum turbulence
• Cooling with a subsonic flow of quantum fluid
• Disentangling temperature and Reynolds number effects in quantum turbulence
• Kolmogorov Cascade as the Governing Mechanism for Intervortex Spacing in Quantum Turbulence
• Small-data global existence of solutions for the Pitaevskii model of superfluidity
• Comment on "On the relations between large-scale models of superfluid helium-4" [Phys. Fluids 33, 127124 (2021]"