Drag on a penetrable two-dimensional disk in a superfluid

The motion of a body through a superfluid can generate phenomena distinct from a normal viscous fluid. This includes the absence of drag below a critical body speed with the shedding of quantised vortices and non-zero drag above this speed. These phenomena are often modelled using the Gross–Pitaevskii (GP) equation, which describes the wavefunction of a weakly interacting Bose–Einstein condensate and its superfluid dynamics. We study the drag experienced by a penetrable circular disk of radius, $a$ , in the form of a two-dimensional potential barrier of height, $V_0$ , that is moving in a superfluid of bulk density, $n_\infty$ , by solving the GP equation. The drag is found to exhibit a unimodal dependence on the disk speed for a fixed value of its barrier height. This behaviour is quantified analytically and confirmed using direct numerical solution. The maximum drag per unit length of $F_{\textit{drag}}^{\textit{max}} \approx 5 a n_\infty V_0$ occurs when the barrier height coincides with the relative kinetic energy of the fluid particles. Flow excitations are diminished at a high particle kinetic energy with a commensurate reduction in the drag. This generates a saddle-node bifurcation in the dynamics of a moving disk under an applied force. These results advance understanding of the motion of bodies with finite penetrability, which is relevant to laser experiments probing the superfluidity of Bose–Einstein condensates.