Visualization Study of Counterflow in Superfluid ${}^4\mathrm{He}$ using Metastable Helium Molecules

Heat is transferred in superfluid ${}^4\mathrm{He}$ via a process known as thermal counterflow. It has been known for many years that above a critical heat current the superfluid component in this counterflow becomes turbulent. It has been suspected that the normal-fluid component may become turbulent as well, but experimental verification is difficult without a technique for visualizing the flow. Here we report a series of visualization studies on the normal-fluid component in a thermal counterflow performed by imaging the motion of seeded metastable helium molecules using a laser-induced-fluorescence technique. We present evidence that the flow of the normal fluid is indeed turbulent at relatively large velocities. Thermal counterflow in which both components are turbulent presents us with a theoretically challenging type of turbulent behavior that is new to physics.

Figure 1

Schematic diagram of the counterflow channel used in the molecule tagging experiment. The pump and probe lasers illuminate the channel at about 6 cm from the tungsten needles.

Figure 2

Typical fluorescent images of a line of helium molecules taken at pump-probe delays of 0, 40, and 80 ms, respectively. A schematic of the widths and the positions of the pump and the probe lasers is also shown. The heat flux is $640\mathrm{mW}/{\mathrm{cm}}^2$. The temperature is 1.95 K. Each image is a superposition of 40 pump-probe trials.

Figure 3

(a) A typical integrated cross-section profile of a molecule line in arbitrary units. The heat flux is $640\mathrm{mW}/{\mathrm{cm}}^2$, and the pump-probe delay is 40 ms. The red line is a Lorentzian fit to the data. (b) The obtained normal-fluid velocity as a function of heat flux at 1.95 K. The black crosses are the data. The solid line shows the calculated velocity based on Eq. (1) in the text.

Figure 4

The square of the width of a molecule line ${\overline{w}}^2(t)$ as a function of drift time $t$ at a heat flux of $277\mathrm{mW}/{\mathrm{cm}}^2$. Error bars are calculated by $2\overline{w}\delta \overline{w}$, where $\delta \overline{w}$ is the associated error in determining the line width $\overline{w}$. The solid curve is a power law fit to the data. The fit formula is shown in the figure with fitting parameters $A$, $B$, and $\gamma$. The best fit value of the power index is $\gamma =4.0\pm 0.3$.

Figure 5

(a) Schematic diagram of the counterflow channel used in the cluster tracking experiment. (b) An image of the square glass tube. A pulsed laser at 905 nm illuminates the needle apexes at about 2 cm from the open end of the channel.

Figure 6

(a) Typical fluorescent images of a cluster of helium molecules taken at 0, 0.1, and 0.2 s after the cluster was created. The heat flux is $119\mathrm{mW}/{\mathrm{cm}}^2$. The temperature is 1.80 K. The exposure time for each image is 20 ms. (b) The obtained normal-fluid velocity as a function of heat flux at 1.80 K. The black crosses are the data. The red line shows the calculated normal-fluid velocity based on Eq. (1) in the text. The blue circles in the inset for the small heat flux regime show the corresponding measured normal-fluid velocity divided by a factor of 2.