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

Abstract

Turbulent drag of an oscillating microsphere that is levitating in superfluid $$^4$$ 4 He at mK temperatures, is unstable slightly above a critical velocity amplitude $$v_c$$ v c . The lifetime $$\tau$$ 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 $$^3$$ 3 He 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 $$f_v$$ f v on $$\Delta v = v - v_c$$ Δ v = v - v c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above $$v_c$$ v c for the onset of turbulent flow: $$f_v = a \,\Delta v$$ f v = a Δ v , where the coefficient a is proportional to the oscillation frequency $$\omega$$ ω above some characteristic frequency $$\omega _k$$ ω k and assumes a finite value for steady motion $$\omega \rightarrow 0$$ ω → 0 . A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.

Quantum viscosity and the Reynolds similitude in quantum liquid He-II

“…The critical velocity u c for vortex generation is regarded as the velocity correction, δu ∼ −u c , in the previous works [7][8][9][10][11]. The existence of the critical velocity for vortex generation is essentially related to an energy barrier between the states with and without a vortex.…”

“…Because of this energy barrier, the transition between the two states follow the first order phase transition and hysteresis can occur with respect to changes in the velocity of the body in our system, depending on the (thermal) fluctuations. Previous studies [7][8][9][10][11] examined the mechanically non-equilibrium states induced by an oscillatory motion of a potential or an object to generate vortices. Here, the velocity of the body can be regarded to change from zero to finite over the critical velocity and then the hysteresis effect can be crucial.…”

“…(1) was replaced as u → u − u c incorporating the critical velocity u c for vortex generation [7]. Despite the qualitative consistency of these predictions with experiments [8][9][10][11], the dynamic similarity has been not established because of u c dependence on the system details. Thus, a universal description of complicated flows interacting with moving bodies in superfluids remains elusive, in contrast to the considerable research on the Reynolds similitude in classical hydrodynamics.…”