Quantum turbulence of bellows-driven4He superflow: Steady state

Abstract

Quantum turbulence in superfluid ${}^{4}$He is studied by the attenuation of second sound in flow channels of 7-mm and 10-mm side square cross sections, and 115-mm length. The ends of the channels are plugged by sintered silver superleaks to allow a pure superflow (i.e., a net flow of the superfluid component only). Flows are generated by mechanically operating a low temperature bellows assembly, as opposed to the helium fountain pump commonly used for previous superflow turbulence studies. The temperature range is $1.35\phantom{\rule{0.28em}{0ex}}\mathrm{K}\ensuremath{\le}T\ensuremath{\le}1.95\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, at the saturated vapor pressure. The observed turbulent steady state is characterized by the vortex line density ${L}^{1/2}=\ensuremath{\gamma}(T)(v\ensuremath{-}{v}_{\mathrm{c}})$, where $v$ is the mean superflow velocity and ${v}_{\mathrm{c}}$ is the critical velocity for the onset of turbulence. The character of the steady state agrees with the Vinen phenomenological model for thermal counterflow turbulence. The coefficient $\ensuremath{\gamma}(T)$ is in fair agreement with previous thermal pure superflow and counterflow experiments. The critical velocity ${v}_{\mathrm{c}}\ensuremath{\approx}0.2$ cm/s is roughly temperature independent.