Effects of Turbulence in He II Thermal Counterflow

Measurement of the damping of small-amplitude transverse vibrations of a fine wire has been used to investigate thermal counterflow of He II in wide channels of rectangular cross section. Below a critical heat current, the damping is independent of the current, and is dictated by laminar viscous flow of normal fluid. At higher heat currents, the damping increases above the subcritical value, and the excess damping has been studied as a function of parameters of the apparatus and liquid. The dependence of the magnitude of the critical heat current on temperature and channel width is described by a critical Reynolds number ${\mathrm{R}}_c=\frac{\rho V_{\mathrm{nc}}d}{\eta }\cong 1200$, where $V_{\mathrm{nc}}$ is the normal fluid velocity corresponding to the critical heat current, $d$ is the channel width, $\eta$ is the normal fluid viscosity, and $\rho$ is the total density. ${\mathrm{R}}_c$ is independent of wire diameter and vibration frequency. The excess damping was found to fit a single empirical expression over a wide range of experimental parameters. An outstanding characteristic of the supercritical damping force is its dependence on the Reynolds number as ${(\mathrm{R}-{\mathrm{R}}_c)}^{\frac{1}{2}}$.