The attenuation of second sound has been used to observe helium-II flow transitions in five annuli in solid-body rotation at 1.40°K. The annuli were 0.6 to 1.9 mm wide, and approximately 15 mm in radius. The onset of attenuation of second sound at the angular velocity ${\Omega }_0$ predicted by Fetter for the creation of a single row of vortex lines established that liquid helium in rotation is able to attain the state of lowest free energy. The onset of attenuation of the second harmonic, which has a velocity node at the middle of an annulus, showed that vortices can be detected away from the median radius at approximately 1.9 ${\mathrm{\Omega }}_0$. In the range $0.65<\mathrm{}\Omega <0.95\mathrm{}$ rad/sec, a critical velocity ${\Omega }_3$ was observed through two effects: First, in annuli in which ${\Omega }_0<{\Omega }_3$, it was usually necessary to rotate faster than ${\Omega }_3$ before the helium would display second-sound attenaution at ${\Omega }_0$. Second, in the narrowest annulus, where ${\Omega }_3<{\Omega }_0$, strong attenuation occurred at ${\Omega }_3$ even though the equilibrium state is vortex-free irrotational flow. The transition at ${\Omega }_3$ is identified with the creation of long-lived vorticity in the helium.

• Received 19 June 1967

DOI:https://doi.org/10.1103/PhysRev.164.262