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

TL;DR

This study investigates vortex ring shedding from an oscillating sphere in superfluid helium-4 below 0.5 K, revealing the origin of turbulent drag force and its intermittent nature near critical velocities.

Contribution

It provides a detailed analysis of turbulent flow onset, identifies the force F1, and links vortex ring shedding to the turbulent drag force in superfluid helium-4.

Findings

Turbulent flow switches intermittently with potential flow.

Mean lifetime of turbulence grows exponentially with force.

Vortex ring shedding explains 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.