Nonlocal energy transfer mechanism in three-dimensional quantum turbulence

Abstract

We investigate the kinetic energy cascade in zero-temperature quantum turbulence. Using simple theoretical arguments and unprecedented numerical simulations, we unveil an universal mechanism transferring energy directly from large to very small scales, thus bypassing the Kolmogorov-like local energy cascade and resulting in nonclassical energy spectra. This mechanism rests both on the vast separation of scales typical of superfluid helium-4 flows and on the alignment between quantum vortices and large-scale velocity gradients, in direct analogy with vortex stretching in classical flows.

Figures (3)

• Figure 1: Visualization of QT simulation in a statistically steady state (run $\varepsilon_{\text{inj}} = 3200$, $a_0 = 10^{-7}$). Quantum vortices are colored by the Gaussian-filtered superfluid vorticity at scale $\ell$, highlighting highly polarized vortex bundles (yellow to red colors).
• Figure 2: Normalized spectral energy fluxes (run $\varepsilon_{\text{inj}} = 3200$, $a_0 = 10^{-7}$). Accumulated energy injection rate $\mathcal{F}_k$ (open circles, Eq. \ref{['eq:forcing_injection_rate']}), total energy flux $\Pi_k$ (filled circles, Eq. \ref{['eq:energy_flux']}), local energy flux $\Pi_k^{<2k}$ (crosses), nonlocal energy flux $\Pi_k^{>k_\ell}$ (squares), and estimated nonlocal flux based on vortex line production $\mathcal{S}_k$ (dashed line, Eq. \ref{['eq:energy_transfer_nonlocal']}). The energy injection scales ($k < k_{\text{f}}$) are highlighted in light red.
• Figure 3: Kinetic energy spectrum from different runs. Two sets of curves are shown with $\ell / a_0 \sim 10^{6}$ (red) and $10^{3}$ (blue), see the End Matter (Table \ref{['tab:simulations']}) for precise values. Different markers correspond to different energy injection rates $\varepsilon_{\text{inj}}$. The spectra are normalized according the analytical prediction $E(k) = (\kappa^2 / 4\pi \ell^2) k^{-1}$ in the quantum scales. Inset: Local energy flux $\Pi_k^{<2k}$ for the different runs.