We study the formation, longevity and breakdown of convective rings during impulsive spin-up in square and cylindrical containers using direct numerical simulations. The rings, which are axisymmetric alternating regions of up- and down-welling flow that can last for O (100) rotation times, were first demonstrated experimentally and arise due to a balance between Coriolis and viscous effects. We study the formation of these rings in the context of the Greenspan-Howard spin-up process, the disruption of which modifies ring formation and evolution. We show that, unless imprinted by boundary geometry, convective rings can only form when the surface providing buoyancy forcing is a free-slip surface, thereby explaining an apparent disagreement between experimental results in the literature. For Prandtl numbers from 1--5 we find that the longest-lived rings occur for intermediate Prandtl numbers, with a Rossby number dependence. Finally, we find that the constant evaporative heat-flux conditions imposed in the experiments are essential in sustaining the rings and in maintaining the vortices that form in consequence of the ring breakdown.

中文翻译：

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瞬态对流自旋动力学

我们使用直接数值模拟研究了方形和圆柱形容器在脉冲旋转过程中对流环的形成、寿命和分解。这些环是向上和向下流动的轴对称交替区域，可以持续 O (100) 次旋转，首先通过实验证明，并且由于科里奥利效应和粘性效应之间的平衡而出现。我们在格林斯潘-霍华德自旋过程的背景下研究这些环的形成，其破坏会改变环的形成和演化。我们表明，除非受到边界几何的印记，否则只有当提供浮力的表面是自由滑动表面时才能形成对流环，从而解释了文献中实验结果之间的明显分歧。对于 1--5 的 Prandtl 数，我们发现寿命最长的环出现在中间的 Prandtl 数中，具有 Rossby 数依赖性。最后，我们发现实验中施加的恒定蒸发热通量条件对于维持环和维持因环破裂而形成的涡流是必不可少的。