The superfluid Reynolds number and the transition from potential flow to turbulence in superfluid 4^4He at mK temperatures

This comment is on Phys.Rev.Lett. 144, 155302 (2015) by M.T. Reeves, T.P. Billam, B.P. Anderson, and A.S. Bradley "Identifying a superfluid Reynolds number via dynamical similarity" where a new superfluid Reynolds number is introduced. This definition is shown to be useful in the data analysis of the finite lifetime of turbulence observed with an oscillating sphere in superfluid helium at mK temperatures in a small velocity interval $\Delta v =(v-v_c)$ just above the critical velocity $v_c$. The very rapid increase of the lifetime with increasing superfluid Reynolds number is compared with the "supertransient" turbulence observed in classical pipe flow.Comment: 3 pages, 1 figur

Vortex Shedding from a Microsphere Oscillating in Superfluid ⁴He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate

Turbulent drag of an oscillating microsphere that is levitating in superfluid ⁴He at mK temperatures, is unstable slightly above a critical velocity amplitude vc. The lifetime τ of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid ³He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency fv on Δv=v−vc is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above vc for the onset of turbulent flow: fv=aΔv, where the coefficient a is proportional to the oscillation frequency ω above some characteristic frequency ωk and assumes a finite value for steady motion ω→0. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence

Extraction of electrons from quantized vortex lines

If electrons are trapped in vortex lines of rotating He II, they can emerge into the vapor phase without overcoming any detectable energy barrier. This observation of the extraction of electrons from straight vortex lines above 1.1°K agrees very well with the evaporation of electrons from vortex rings studied by Surko and Reif below 0.7°

Non-ohmic conduction in doped polyacetylene at low temperatures

The electrical conductivity of a iodine-doped polyacetylene is measured as a function of the electric field Escr at temperatures between 4K and 0.3K. We find that after an initial non-linear behavior sgr increases linearly with Escr in agreement with a theoretical description based on variable-range hopping conduction. The non-linear rise at low fields depends on the iodine concentration. In heavily doped samples the increase is small and varies as Escr2, whereas in less conductive samples a large change is observed at 0.3K which varies approximately as log Escr for fields from 1 V/m to 150 V/m

Variable-range hopping conduction in doped germanium at very low temperatures and high magnetic fields

The conductivity of doped Ge below the metal-insulator transition is measured at temperatures between 4 K and 40 mK and in magnetic fields up to 7 Tesla. In zero field the resistivity exponent diverges asT –1/2. In weak fields the magnetoresistance increases asB 2 and becomes exponentially large in strong fields and at low temperatures. The results can be described quantitatively in terms of variable-range hopping between localized states having a Coulomb gap in the density of states at the Fermi level. The magnetoresistance is calculated for arbitrary fields by means of a quasi-classical method. A fit to the data gives the radius of the localized states and the density of states. The sample is found to be very close to the metal-insulator transition. A small increase of the binding energy is observed in strong fields

The superfluid Reynolds number and the transition from potential flow to turbulence in superfluid He-4 at mK temperatures

This comment is on Phys. Rev. Lett. 144, 155302 (2015) by M.T. Reeves, T.P. Billam, B.P. Anderson, and A.S. Bradley "Identifying a superfluid Reynolds number via dynamical similarity" where a new superfluid Reynolds number is introduced. This definition is shown to be useful in the data analysis of the finite lifetime of turbulence observed with an oscillating sphere in superfluid helium at mK temperatures in a small velocity interval Δ v =(v-vc) just above the critical velocity vc. The very rapid increase of the lifetime with increasing superfluid Reynolds number is compared with the "supertransient" turbulence observed in classical pipe flow

Vortex nucleation, transition to turbulence, and caviation: ‚system failure’ experiments in liquid helium and extreme value statistics

It is suggested that recent experiments in liquid helium, like single vortex nucleation, transition to turbulent flow around a sphere at a critical velocity, and cavitation of the liquid in a sound wave belong to the type of “system failure” experiments which is well known in reliability testing and whose statistical properties are described by extreme value statistics. This leads to far reaching consequences for the interpretation of the critical velocities and of the voltage threshold for cavitation

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

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.Comment: 7 pages, 4 figures. Extended version of DOI 10.1007/s10909-013-0888-4 Journal of Low Temperature Physics, Online First, 201