# Turbulent radial thermal counterflow in the framework of the HVBK model

## TL;DR

This paper models turbulent radial counterflow in superfluid helium using the HVBK equations, revealing the importance of temperature-dependent properties and boundary layer formation in steady-state solutions.

## Contribution

It introduces a detailed HVBK-based model for turbulent superfluid counterflow, emphasizing the role of temperature variations and boundary layers.

## Key findings

- Existence of steady solutions depends on temperature-dependent properties.
- Thermal boundary layer thickness increases with surface temperature.
- Flow analysis includes vortex line density distribution.

## Abstract

We apply the coarse-grained Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equations to model the statistically steady-state, turbulent, cylindrically symmetric radial counterflow generated by a moderately large heat flux from the surface of a cylinder immersed in superfluid $^4$He. We show that a time-independent solution exists only if a spatial non-uniformity of temperature and the dependence on temperature of the thermodynamic properties are accounted for. We demonstrate the formation of a thermal boundary layer whose thickness grows with temperature of the cylinder's surface, and analyze the properties of the flow in the radial direction, including the local average vortex line density.