Quantum vortices leave a macroscopic signature in the normal fluid

Abstract

Recent work has highlighted the remarkable properties of quantum turbulence in superfluid helium II, consisting of a disordered tangle of quantised vortex lines which interact with each other and reconnect when they collide. According to Landau's two-fluid theory, these vortex lines move in a surrounding of thermal excitations called the normal fluid. Until now, the normal fluid has often been considered a passive background which simply provides the vortex lines with a mechanism for dissipating their kinetic energy into heat. Using a model which fully takes into account the two-way interaction between the vortex lines and the normal fluid, here we show numerically that each vortex line creates a macroscopic wake in the normal fluid that can be larger than the average distance between vortex lines; this is surprising, given the microscopic size of the superfluid vortex cores which induce these wakes. We show that in heat transfer experiments, the flow of the normal fluid can therefore be described as the superposition of an imposed uniform flow and wakes generated by the vortex lines, leading to non-classical statistics of the normal fluid velocity. We also argue that this first evidence of independent fluid structures in the thermal excitations postulated by Landau may be at the root of recent, unaccounted for, experimental findings.

Figures (9)

• Figure 1: Snapshots of vortex tangles. Turbulence at $T=1.5~\rm K$ generated by counterflow velocities $v_{ns}^{(1)}= 0.27 \rm cm/s$ (left) and $v_{ns}^{(2)}= 0.94 \rm cm/s$ (right). The superfluid vortex lines are displayed as green curves and the normal fluid dipoles are visualized by the normalised enstrophy $\Omega(\mathbf{x})/\Omega_{max}$ in reddish color. The relative magnitude of normal fluid fluctuations $\Delta v_n (x,z)$ is plotted on a $xz$ plane at constant $y$.
• Figure 2: PDFs of velocity fluctuations. Calculations at $T=1.5~{\rm K}$ at the same parameters as Fig. \ref{['fig1']}. Left: streamwise PDF$(\delta v_n^z)$ vs $\delta v_n^z/\sigma_z$ where $\sigma_z$ is the standard deviation. Right: spanwise PDF$(\delta v_n^x)$ vs $\delta v_n^x/\sigma_x$ where $\sigma_x$ is the standard deviation. Red curves refer to $v_{ns}^{(1)}=0.27 \rm cm/s$ and green curves to $v_{ns}^{(2)}=0.94 \rm cm/s$. Gaussian distributions are showed in dot-dashed dark blue line for reference. Dashed cyan curves are exponential fits to the wide tails. Insets. Left (right): streamwise (spanwise) normalised standard deviation $\sigma_z/v_{ns}$ ($\sigma_x/v_{ns}$) as a function of temperature $T$. Colors as in main figure.
• Figure 3: Single vortex wake. Temperature $T=1.5~\rm K$ and $v_{ns}^{(1)}=0.27 \rm cm/s$ Left column: relative normal fluid streamwise velocity fluctuations $\Delta v_n^z=\delta v_n^z/\bar{v}_n^z=(v_n^z(x,z)-\bar{v}_n^z)/\bar{v}_n^z$ vs $x$ and $z$ at fixed $y_0$. The ruler indicates the direction of the relative velocity of the single vortex line with respect to the normal fluid. Centre column: PDF$(\delta v_n^z)$ vs $\delta v_n^z/\sigma_z$, where $\delta v_n^z=v_n^z-\bar{v}_n^z$ and $\sigma_z$ is the standard deviation. Right column: PDF$(\delta v_n^x)$ vs $\delta v_n^x/\sigma_x$, where $\delta v_n^x=v_n^x$ ($\bar{v}_n^x=0$) and $\sigma_x$ is the standard deviation. Gaussian distributions are showed in dot-dashed dark blue line for reference. The dashed cyan lines are exponential functions to guide the eye.
• Figure 4: Vortex statistics. Parameters: $T=1.5~\rm K$, $v_{ns}=v_{ns}^{(2)}=0.94~\rm cm/s.$ Distribution of streamwise vortex velocity fluctuations ${\rm PDF}(\delta v_L^z)$ vs $\delta v_L^z/\sigma_{v_L^z}$ where $\sigma_{v_L^z}$ is the standard deviation of $v_L^z$. The dot-dashed blue line is the Gaussian fit, and the cyan dahed line is a guide to the eyes to highlight the tail.
• Figure 5: Single vortex wake. Temperature $T=1.5~\rm K$ and $v_{ns}^{(2)}=0.94 \rm cm/s$ Left column: relative normal fluid streamwise velocity fluctuations $\Delta v_n^z=\delta v_n^z/\bar{v}_n^z=(v_n^z(x,z)-\bar{v}_n^z)/\bar{v}_n^z$ vs $x$ and $z$ at fixed $y_0$. The ruler indicates the direction of the relative velocity of the single vortex line with respect to the normal fluid. Centre column: PDF$(\delta v_n^z)$ vs $\delta v_n^z/\sigma_z$, where $\delta v_n^z=v_n^z-\bar{v}_n^z$ and $\sigma_z$ is the standard deviation. Right column: PDF$(\delta v_n^x)$ vs $\delta v_n^x/\sigma_x$, where $\delta v_n^x=v_n^x$ ($\bar{v}_n^x=0$) and $\sigma_x$ is the standard deviation. Gaussian distributions are showed in dot-dashed dark blue line for reference. The dashed cyan lines are exponential functions to guide the eye.