Coflow turbulence of superfluidHe4in a square channel: Vortices trapped on a cylindrical attractor

Abstract

We perform a numerical simulation of the dynamics of quantized vortices produced by coflow in a square channel using the vortex filament model. Unlike the situation in thermal counterflow, where the superfluid velocity vs and normal fluid velocity vn flow in opposite directions, in coflow, vs and vn flow in the same direction. Quantum turbulence in thermal counterflow has been long studied theoretically and experimentally, and its various features have been revealed. In recent years, an experiment on quantum turbulence in coflow has been performed to observe different features of thermal counterflow. By supposing that vs is uniform and vn takes the Hagen-Poiseuille profile, which is different from the experiment where vn is thought to be turbulent, we calculate the coflow turbulence. Vortices preferentially accumulate on the surface of a cylinder for vs ≃ vn by mutual friction; namely, the coflow turbulence has an attractor. How strongly the vortices are attracted depends on the temperature and velocity. The length of the vortices increases as the vortices protruding from the cylindrical attractor continue to wrap around it. As the vortices become dense on the attractor, they spread toward its interior by their repulsive interaction. Then, the superfluid velocity profile induced by the vortices gradually mimics the normal-fluid velocity profile. This is an indication of velocity matching, which is an important feature of coflow turbulence.

Fully Coupled Two-Fluid Dynamics in Superfluid He4 : Anomalous Anisotropic Velocity Fluctuations in Counterflow

“…Coupled dynamics of quantized vortices and normal fluid.-The VFM is used as one of the most powerful tools to describe the dynamics of quantized vortices [20,[46][47][48][49][50][51][52][53][54][55][56]. The position vector s of the filaments are represented by the parametric form s = s(ξ) with arc length ξ.…”