We perform a numerical analysis of counterflow quantum turbulence of superfluid ${}^4\mathrm{He}$ with nonuniform flows by using the vortex filament model. In recent visualization experiments nonuniform laminar flows of the normal fluid, namely, Hagen-Poiseuille flow and tail-flattened flow, have been observed. Tail-flattened flow is a laminar flow in which the outer part of the Hagen-Poiseuille flow becomes flat. In our simulation, the velocity field of the normal fluid is prescribed to be two nonuniform profiles. This work addresses a square channel to obtain important physics not revealed in the preceding numerical works. In the studies of the two profiles we analyze the statistics of the physical quantities. Under Hagen-Poiseuille flow, inhomogeneous quantum turbulence appears as a statistically steady state. The vortex tangle shows a characteristic space-time oscillation. Under tail-flattened flow, the nature of the quantum turbulence depends strongly on that flatness. Vortex line density increases significantly as the profile becomes flatter, being saturated above a certain flatness. The inhomogeneity is significantly reduced in comparison to the case of Hagen-Poiseuille flow. Investigating the behavior of quantized vortices reveals that tail-flattened flow is an intermediate state between Hagen-Poiseuille flow and uniform flow. In both profiles we obtain a characteristic inhomogeneity in the physical quantities, which suggests that a boundary layer of superfluid appears near a solid boundary. The vortex tangle produces a velocity field opposite to the applied superfluid flow, and, consequently, the superfluid flow becomes smaller than the applied one.

• Received 23 February 2015
• Revised 21 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.184504