Solutions of the Eliassen balance equation for inertially and/or symmetrically stable and unstable vortices,Quarterly Journal of the Royal Meteorological Society

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Solutions of the Eliassen balance equation for inertially and/or symmetrically stable and unstable vortices
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-05-08 , DOI: 10.1002/qj.4098
Shanghong Wang _{1,

2} , Michael T. Montgomery ₃ , Roger K. Smith ₁

Affiliation

Two methods for solving the Eliassen equation for the corresponding balanced secondary circulation of a numerically simulated, high-resolution tropical cyclone vortex are compared. In idealized calculations for a symmetrically stable vortex, both methods (successive overrelaxation [SOR] and multigrid) converge and the solutions are broadly similar. In more typical cases, where the vortex has regions of inertial or symmetric instability, it is necessary to coarsen the data from the numerical simulation to determine the balanced secondary circulation. A convergent solution can be obtained with the multigrid method for a finer grid spacing than with the SOR method. However, the multigrid method fails to converge when the vertical grid spacing is similar to that of the numerical simulation. Results using both methods confirm the inability of the balance formulation to capture the strong inflow and resulting tangential wind spin-up in the frictional boundary layer during a period of rapid intensification. Typical tropical cyclone simulations show an inflow layer just beneath the upper-level outflow layer, and the corresponding balanced secondary circulation may show such an inflow layer also. However, caution is called for in attributing this inflow layer to a balanced flow response driven by the distribution of diabatic heating and tangential momentum forcing. Our study suggests that this inflow layer is likely an artifact of the ad hoc regularization procedure that is necessary to keep the Eliassen equation globally elliptic in regions of inertial and/or symmetric instability.

中文翻译：

惯性和/或对称稳定和不稳定涡流的埃利亚森平衡方程的解

比较了求解数值模拟的高分辨率热带气旋涡的相应平衡二次环流的 Eliassen 方程的两种方法。在对称稳定涡流的理想化计算中，两种方法（连续过度松弛 [SOR] 和多重网格）收敛并且解决方案大致相似。在更典型的情况下，涡流具有惯性或对称不稳定性区域，有必要对数值模拟的数据进行粗化，以确定平衡的二次循环。对于比 SOR 方法更精细的网格间距，使用多重网格方法可以获得收敛解。然而，当垂直网格间距与数值模拟相似时，多重网格方法无法收敛。使用这两种方法的结果证实了平衡公式无法在快速强化期间捕捉摩擦边界层中的强流入和由此产生的切向风自旋。典型的热带气旋模拟显示在上层流出层正下方有一个流入层，相应的平衡二次环流也可能显示出这样的流入层。然而，在将这个流入层归因于由非绝热加热和切向动量强迫的分布驱动的平衡流动响应时需要谨慎。我们的研究表明，这个流入层很可能是临时正则化程序的产物，这是在惯性和/或对称不稳定性区域中保持 Eliassen 方程全局椭圆所必需的。

更新日期：2021-05-08

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