Title: Spontaneous vortex crystal formation in classical rotating flows Show Chinese title

Title: 经典旋转流中自发涡旋晶体的形成

Abstract: Vortex crystals, ordered structures observed in superconductors and rotating superfluids, have also been hypothesized to form in classical fluids, based on numerical simulations and observations of the Jovian polar atmospheres. We perform direct numerical simulations of the Navier-Stokes equations in rotating frames, to investigate the spontaneous emergence of metastable vortex crystals. We analyze the energy spectrum, vortex morphology, and spatio-temporal dynamics to understand their roles in crystal formation and evolution. In addition, we explore domains with varying aspect ratios to examine their impact on the vortex lattice. Our results indicate a relationship between the crystal lifespan and dissipation, and we propose a scaling law linking the rotation rate, domain geometry, and vortex lattice periodicity. Finally, we identify a critical threshold in the control parameter, the Rossby number, suggesting a behavior similar to that found in phase transitions. Show Chinese abstract

Abstract: 涡旋晶体是在超导体和旋转超流体中观察到的有序结构，也基于数值模拟和木星极地大气的观测，假设在经典流体中也会形成。我们对旋转参考系中的纳维-斯托克斯方程进行直接数值模拟，以研究亚稳态涡旋晶体的自发出现。我们分析能量谱、涡旋形态和时空动力学，以了解它们在晶体形成和演化中的作用。此外，我们探索了不同长宽比的区域，以检查其对涡旋晶格的影响。我们的结果表明晶体寿命与耗散之间存在关系，并提出了一个将旋转速率、区域几何形状和涡旋晶格周期性联系起来的标度定律。最后，我们在控制参数罗斯比数中识别出一个临界阈值，表明其行为类似于相变中发现的行为。