Shedding of Vortex Rings from an Oscillating Sphere in Superfluid He-4 below 0.5 K - The Origin of the Turbulent Drag Force

Abstract

The onset of turbulent flow around an oscillating sphere is known to occur at a critical velocity vc ~ sqrt(kappa omega) where kappa is the circulation quantum and omega is the oscillation frequency. However, in a small interval of driving force amplitudes F (or corresponding velocity amplitudes of few percent above vc) the turbulent flow is found to be unstable. The flow pattern switches intermittently between potential flow and turbulence. The lifetimes of the turbulent phases have an exponential distribution and the mean lifetimes tau grow very rapidly with increasing driving force, namely as tau(F) ~ exp [(F/F1)^2]. In this work this experimental result is analyzed in more detail than before, in particular the force F1 is identified. As a result, the turbulent drag force F(v) ~ (v^2 - vc^2) can be ascribed quantitatively to the shedding of vortex rings having the size of the sphere. Moreover, we can infer the average number of vortex rings that are shed per half-period at any given velocity v on the turbulent drag force.