Inverse energy transfer in three-dimensional quantum vortex flows

Abstract

Vortex reconnections play a fundamental role in fluids.They increase the complexity of flow and develop small-scale motions.In this work, we report that in superfluids, they can also excite large scales. We numerically illustrate that during a superfluid vortex reconnection energy is injected into the thermal (normal) component of helium~II at small length scales, but is transferred nonlinearly to larger length scales, increasing the integral length scale of the normal fluid. We show, by studying about fifty different reconnections, that this inverse energy transfer is triggered by the helical imbalance generated in the normal fluid flow by the mutual friction force coupling the superfluid vortices and the normal component. We finally discuss the relevance of our findings to the problem of superfluid turbulence.

Figures (7)

• Figure 1: Three-dimensional rendering of the time evolution of an initially orthogonal superfluid vortex configuration undergoing a reconnection at $t=t_R$. Temperature is $T = 1.9$K and time is made dimensionless with $\tau_R = L^2/\kappa$. Green tubes represent the superfluid vortex lines (the tubes’ radii have been greatly exaggerated for visual purpose). In the top sequence, the blue volume rendering represents the scaled normal fluid enstrophy $\boldsymbol{\omega}^2/\boldsymbol{\omega}^2_{max}$. Note the Kelvin wave on the superfluid vortex at $(t-t_R)/\tau_R\approx0.001$. In the bottom sequence, the red/blue volume rendering at the same times represent scaled positive/negative normal fluid helicity.
• Figure 2: (a): Temporal evolution of the total normal fluid helicity $\mathcal{H}$, normalised by the quantum of circulation $\kappa$. Bold solid lines refer to orthogonal reconnections, slightly faded lines refer to the set of Hopf-links reconnections. Red color refers to $T=1.9K$, blue to $T=2.1K$. (b): Normal fluid kinetic energy spectrum $E(k)$ before reconnection (dashed lines), at reconnection (solid lines) and after reconnection (dotted lines), for a pair of initially orthogonal vortices. Red (blue) lins correspond to $T=1.9K$ ($T=2.1K$).
• Figure 3: (a): Spectral normal fluid kinetic energy flux, $\Pi (k)$ for orthogonal reconnections. Times and temperatures are labelled as in Fig. \ref{['fig:total-helicity']} (b). (b): Post reconnection temporal evolution of the integral length scale, $L_0(t)$ scaled by the reconnection time integral scale $L_R=L_0(t_R)$. Slightly faded lines refer to the set of Hopf-links reconnections (left axis) and bold solid lines refer to orthogonal reconnections (right axis). Red (blue) lins correspond to $T=1.9K$ ($T=2.1K$).
• Figure 4: Temporal evolution of the ratio of helically-projected mutual friction force components $f^\pm$, for orthogonal reconnections. Inset: temporal evolution of total helical components.
• Figure 5: Schematic diagram of the orthogonal vortex configuration.