论文标题
b {é}在缓慢旋转的一分钱圆柱体中的对流，约有恒定的热通量边界条件
B{é}nard convection in a slowly rotating penny shaped cylinder subject to constant heat flux boundary conditions
论文作者
论文摘要
我们考虑在浅缸半径，L和深度H（<< l）中轴对称性Boussinesq对流，该轴向对称性$ω$在其对称性轴上旋转，其对称轴与垂直方向排列。采用恒定的热通量边界条件（顶部和底部），如果$ω$足够小，则在长度长度尺度上发生不稳定性的发作。我们通过建立良好的两尺度渐近扩张方法研究了非线性发展。将结果与原始管理方程式的直接数值模拟（DNS）进行比较，在足够大的prandtl数字（$σ$）方面很好。随着$σ$的减少，渐近学的有限振幅范围会降低。尽管DNS预测的大量子午对流电池被渐近流量充分近似，但方位角流量几乎是灾难性的，因为在小$σ$处的显着角动量转运，圆柱形几何形状加剧了。为了评估情况，我们提出了基于从渐近学衍生的子午流函数$ψ$建立的混合方法。使用$ψ$，我们解决了DNS的方位速度V的现在线性方位运动方程。我们的“混合”方法使我们能够解释Oruba，Davidson \＆Dormy先前发现的流量的特征（J. Fluid Mech。，第812卷，2017年，2017年，第890-904页）。
We consider axisymmetric Boussinesq convection in a shallow cylinder radius, L, and depth, H (<< L), which rotates with angular velocity $Ω$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $Ω$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at sufficiently large Prandtl number, $σ$. As $σ$ is reduced, the finite amplitude range of applicability of the asymptotics reduces in concert. Though the large meridional convective cell, predicted by the DNS, is approximated adequately by the asymptotics, the azimuthal flow fails almost catastrophically, because of significant angular momentum transport at small $σ$, exacerbated by the cylindrical geometry. To appraise the situation, we propose hybrid methods that build on the meridional streamfunction $ψ$ derived from the asymptotics. With $ψ$ given, we solve the now linear azimuthal equation of motion for the azimuthal velocity v by DNS. Our ''hybrid'' methods enable us to explain features of the flow at large Rayleigh number, found previously by Oruba, Davidson \& Dormy (J. Fluid Mech.,vol. 812, 2017, pp. 890-904).
