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

AbstractTurbulent 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.