Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

• Published in: Journal of low temperature physics Vol. 156; no. 3-6; pp. 116 - 131
• Main Authors: Bradley, D. I., Fear, M. J., Fisher, S. N., Guénault, A. M., Haley, R. P., Lawson, C. R., McClintock, P. V. E., Pickett, G. R., Schanen, R., Tsepelin, V., Wheatland, L. A.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.09.2009
• Subjects: Characterization and Evaluation of Materials; Condensed Matter Physics; Magnetic Materials; Magnetism; Physics; Physics and Astronomy; Turbulence; 47.27.Cn; Superfluid; 67.25.dk; Critical velocity; Tuning fork; 67.25.dg
• ISSN: 0022-2291; 1573-7357
• DOI: 10.1007/s10909-009-9901-3

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4 He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.