Turbulent drag of an oscillating microsphere that is levitating in superfluid He-4 at mK temperatures, is unstable slightly above a critical velocity amplitude v(c). The life-time tau 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 He-3 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) on Delta 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) for the onset of turbulent flow: f(v) = a Delta v, where the coefficient a is proportional to the oscillation frequency omega above some characteristic frequency omega(k) and assumes a finite value for steady motion omega -> 0. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.