Abstract
The critical velocity v c for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (ω/2π from 100 Hz to 700 Hz) and is described by \(v_{c}=2.6\sqrt{\kappa \omega}\) , where κ is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives \(v_{c}\approx \sqrt{8\kappa \omega/\beta}\) , where β∼1 depends on the coefficients of mutual friction. This agrees well with the data and implies that v c is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with v c obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.
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Hänninen, R., Schoepe, W. Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow. J Low Temp Phys 153, 189–196 (2008). https://doi.org/10.1007/s10909-008-9834-2
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DOI: https://doi.org/10.1007/s10909-008-9834-2