We investigate a procedure to generate turbulence in a trapped Bose-Einstein condensate which takes advantage of the decay of multicharged vortices to reduce surface oscillations. We show that the resulting singly charged vortices twist around each other, intertwined in the shape of helical Kelvin waves, which collide and undergo vortex reconnections, creating a disordered vortex state. By examining the velocity statistics, the energy spectrum, the correlation functions, and the temporal decay and comparing these properties with the properties of classical turbulence and observations in superfluid helium, we conclude that this disordered vortex state can be identified with the Vinen regime of turbulence which has been discovered in the context of superfluid helium.
Vortex Shedding from a Microsphere Oscillating in Superfluid
4He 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
vc v c . The lifetime
τ 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
fv f v on
Δv=v−vc 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
vc v c for the onset of turbulent flow:
fv=aΔv f v = a Δ v , where the coefficient a is proportional to the oscillation frequency
ω ω above some characteristic frequency
ωk ω k and assumes a finite value for steady motion
ω→0 ω → 0 . A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.
We report the experimental generation of two-dimensional quantum turbulence in dilute-gas Bose-Einstein condensates by stirring the condensate with a laser beam, and the decay of the turbulent state to a large-scale flow in the form of a persistent current in a toroidal trap geometry. From numerical simulations of the stirring process, we characterize the dynamics of the quantized vortices in the condensate, and analyze the kinetic energy spectrum. Our observations are consistent with basic features of two-dimensional turbulence in classical incompressible fluids.