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

DI Bradley, MJ Fear, SN Fisher, AM Guénault… - Journal of Low …, 2009 - Springer
DI Bradley, MJ Fear, SN Fisher, AM Guénault, RP Haley, CR Lawson, PVE McClintock
Journal of Low Temperature Physics, 2009Springer
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 …
Abstract
We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4He, 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.
Springer
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