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arXiv:cond-mat/9507024

"Classical" Vortex Nucleation in Superflow Through Small Orifices

Ajit Mohan Srivastava, Stone, Michael

Published Jul 9, 1995• 0 citations
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Abstract

We report on numerical solutions of the Gross-Pitaevskii equation for two-dimensional flow of a superfluid condensate through a small orifice. Above a critical velocity of about $30\%$ of the speed of sound, cavitation occurs in the throat of the orifice. The cavitating bubbles form the cores of singly quantized vortices which detach from the boundary and are convected downstream.

DOI
10.48550/arxiv.cond-mat/9507024

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We report on numerical solutions of the Gross-Pitaevskii equation for two-dimensional flow of a superfluid condensate through a small orifice. Above a critical velocity of about 30%30\%30% of the speed of sound, cavitation occurs in the throat of the orifice. The cavitating bubbles form the cores of singly quantized vortices which detach from the boundary and are convected downstream.
The flow of a superfluid past a solid boundary can generate vortices, with a key criterion being that the local flow speed reaches the speed of sound (Landau). However, the physical mechanism underlying this vortex generation remains unresolved. We consider the canonical problem of uniform flow past an impenetrable planar wall, to examine the vortex nucleation process generated by a solid obstruction moving through a superfluid. A linear stability analysis is conducted of this uniform two-dimensional flow governed by the Gross–Pitaevskii equation (GPE). This shows that the flow is marginally stable to two-dimensional, normal-mode perturbations. Direct numerical solutions of the GPE confirm this finding for small perturbations of finite amplitude. They also reveal the existence of a critical amplitude above which instabilities, in the form of vortices, are nucleated at the solid wall in finite time. Once nucleated, these vortices convect away from the solid wall with infinite initial speed. The physical mechanism underlying this nonlinear phenomenon is discussed, and a proposal is advanced to deepen its understanding.
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© The Author(s) 2024. We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
Abstract We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.
Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be 28+/-1 healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.