Dynamic similarity of vortex shedding in a superfluid flowing past a penetrable obstacle

Abstract: We numerically investigate wake dynamics in a superfluid flowing past a penetrable obstacle. Unlike an impenetrable object, a penetrable obstacle does not fully deplete the density. We define an effective diameter D_eff from the Mach-1 contour of the time-averaged irrotational flow around the obstacle, which delineates the local supersonic region where quantized vortices nucleate. Using this flow-defined length scale, we construct a superfluid Reynolds number Re_s = (v0 minus vc) times D_eff divided by (hbar over m), where v0 is the flow speed, vc is the critical velocity, and m is the particle mass. We show that Re_s organizes the wake dynamics across obstacle sizes and strengths: the transition from dipole-row emission to alternating vortex cluster shedding occurs at Re_s around 2, and both the Strouhal number and the drag coefficient collapse onto universal curves when plotted as functions of Re_s. These results extend the concept of dynamic similarity in superfluid flows to penetrable obstacles and demonstrate that the dynamically relevant length scale is determined by the supersonic region rather than by the geometric obstacle size.