Visualization study of the law of the wall in superfluid helium-4

The discovery of the "law of the wall" is a significant milestone in fluid dynamics research. It explains the logarithmic form of the mean velocity in turbulent, high Reynolds number, no slip, boundary layer flows. However, this law may not be applicable to superfluid helium-4 (He II), which consists of two fluid components: a viscous normal fluid adhering to the “no slip" condition, and an inviscid superfluid unrestricted by such a condition. Previous studies have revealed quasiclassical behavior in mechanically driven He II flows due to a strong, mutual friction dependent coupling of the two fluids. Nevertheless, it remains uncertain whether this coupling is effective in the thin boundary layer, where a strong velocity gradient exists and any mismatch between velocities could alter the classical law of the wall. Understanding the near-wall velocity profile in He II expands our knowledge of turbulence and provides a foundation for friction factor modeling in He II pipe flows. Such knowledge is critical for the design of efficient He II-cooled particle accelerators and superconducting magnets. Here, we present a flow visualization study of the near-wall velocity profile in He II pipe flows using molecular tagging velocimetry at Reynolds numbers exceeding 10⁶. We provide evidence of the log-law near-wall velocity profile in He II, albeit with a Kármán's constant that is less than half the value observed in classical fluids.