Hysteresis in quantized vortex shedding

Abstract

It is shown using numerical simulations that flow patterns around an obstacle potential moving in a superfluid exhibit hysteresis. In a certain velocity region, there is a bistability between stationary laminar flow and periodic vortex shedding. The bistability exists in two and three dimensional systems.

Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

“…However, no periodic vortex shedding is observed with the impenetrable obstacle and the number of vortex dipoles grows monotonically once the first vortex dipole is emitted. This means that the subsequent vortex generations are significantly affected by the presence of the first vortex dipole [23,27]. It is noted that for v = 1.90 mm/s in Fig.…”

“…A highly oblate BEC of 23 Na atoms is prepared in a hybrid trap composed of a pancake-shaped optical trap and a magnetic quadruple trap. The trapping frequencies are ω r,z = 2π × (9.0, 400) Hz and the atom number in the condensate is N 0 = 3.3(2) × 10 6 , giving the chemical potential µ ≈ h × 1.0 kHz, where h is the Planck constant.…”

“…Hence, it is possible for vortices to be emitted individually into the condensate. The individually emitted vortices would disturb the superfluid velocity field around the obstacle more strongly than a vortex dipole, leading to irregular vortex shedding or possibly more intriguing shedding patterns such as the Bénard-von Kármán vortex street [22,23].…”

“…On the other hand, the first vortex dipole from a penetrable obstacle usually propagates along the moving direction of the obstacle. Symmetric periodic array of vortex dipoles are known to be unstable towards staggered configurations of vortex dipoles [22,23,28], which were typically observed in the experiment when multiple vortex dipoles were generated [Figs. 5(d) and (e)].…”

“…Because there is no density-depleted region in the condensate, it is ensured that a vortex and an antivortex would be created at the same time into the condensate. On the other hand, in the impenetrable case, there is a density-depleted region occupied by the obstacle such that a vortex can be individually emitted into the condensate, while the other vortex that is created as a partner of the emitted vortex still remains in the density-depleted region [22,23]. The individual vortex emission might be induced by small fluctuations in superfluid flow, braking the mirror symmetry of the system with respect to the obstacle moving direction.…”