Transition from laminar to turbulent drag in flow due to a vibrating quartz fork

Flow due to a commercially available vibrating quartz fork is studied in gaseous helium, He I and He II, over a wide range of temperatures and pressures. On increasing the driving force applied to the fork, the drag changes in character from laminar (characterized by a linear drive vs velocity dependence) to turbulent (characterized by a quadratic drive vs velocity dependence). We characterize this transition by a critical Reynolds number Re-cr(delta)=U-cr delta/nu, where U-cr is the critical velocity, nu stands for the kinematic viscosity, delta=root 2 nu/omega is the viscous penetration depth, and omega is the angular frequency of oscillations. We have experimentally verified that the corresponding scaling U-cr proportional to root nu omega holds in a classical viscous fluid over two decades of nu.