Dynamic similarity of vortex shedding in atomic Bose-Einstein condensate

We numerically investigate the dynamic similarity of vortex shedding in atomic Bose-Einstein Condensates (BECs) using the two-dimensional Gross-Pitaevskii equation with a moving Gaussian potential. By comparing the local sound velocity with the flow speed around the potential barrier, we estimate the dynamic effective diameter of the Gaussian potential for both penetrable and impenetrable potentials. As the velocity of the flow around the potential barrier increases, the dynamic effective diameter correspondingly increases further, which aligns with the vortex formation region observed in real space. Furthermore, we investigate the drag and lift forces exerted by the Gaussian potential, relating them to the superfluid Reynolds number derived from the estimated dynamic effective diameter. The drag force is proportional to the velocity minus the critical velocity at which vortex shedding initiates, and the modified drag coefficient demonstrates a universal behavior with respect to the superfluid Reynolds number, paralleling its counterpart in classical fluid dynamics. The frequency of the oscillation in the lift force also exhibits a universal trend, even in the penetrable potential. Our study enhances the understanding of quantum fluid in relation to classical fluid dynamics.