拐角处的超流
Superflows around corners
AI总结：
研究通过解析和数值方法探讨了超流在有限尺寸障碍物拐角处的动力学，揭示了尖锐拐角对涡旋成核临界流速的关键作用，并为超流稳定性提供了理论框架。
摘要：
我们通过解析和数值方法研究了由Gross-Pitaevskii方程支配的二维超流在经过有限尺寸矩形障碍物（一个不可穿透的墙和一个不可穿透的矩形阱）时的动力学。在扩展经典研究的基础上，我们关注尖锐拐角在涡旋成核起始点的作用。利用基于复势流的Schwarz-Christoffel方法和数值模拟相结合的分析技术，我们表明局部速度放大在尖锐拐角附近对涡旋成核的临界流速起关键作用。对于墙和阱配置，我们解析和理论地确定了临界速度作为障碍物宽度及其高度或深度的函数，发现理论与数值模拟之间有很好的一致性。我们的结果提供了一个简单的框架，用于理解具有尖锐特征的有限尺寸障碍物后的超流稳定性，并直接相关于原子玻色-爱因斯坦凝聚体及相关超流系统中的实验可实现配置。
英文摘要：
We investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, we focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, we show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, we identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding an excellent agreement between the theory and our numerical simulations. Our results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features and are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems.
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