Some effects of horizontal discretization on linear baroclinic and symmetric instabilities
Some effects of horizontal discretization on linear baroclinic and symmetric instabilities
复制标题
水平离散化对线性斜压和对称不稳定性的一些影响
DOI：
10.1016/j.ocemod.2018.03.004
复制
发表时间：
2018
期刊：
影响因子：
3.2
通讯作者：
I. Grooms
中科院分区：
文献类型：
--
作者：
W. Barham;S. Bachman;I. Grooms
通过分析 B 和 C 网格上海洋模型中静水 Eady 问题的行为，研究了水平离散化对线性斜压和对称不稳定性的影响。在 C 网格上，小波长处会出现虚假的斜压不稳定性。这种不稳定性并不会随着网格规模的减小而消失；相反，它只是移动到较小的水平尺度。随着网格规模的减小，寄生不稳定性的峰值增长率与网格规模无关。它等于 c f/Ri，其中 Ri 是平衡理查森数，f 是科里奥利参数，c 是取决于理查森数的无量纲常数。随着理查森数的增加，c 增加到大约 1/2 的上限；对于大理查森数，虚假不稳定比 Eady 不稳定更快。为了抑制虚假不稳定性，建议使用四阶中心示踪平流以及双调和粘度和扩散，系数为 (Δ x) 4 f/(32 Ri) 或更大，其中 Δ x 是网格比例。在B网格上，斜压和对称不稳定性的增长率太小，并且随着网格尺度的减小而向上收敛到正确值；没有观察到虚假的不稳定性。在允许涡流分辨率的 B 网格模型中，斜压不稳定性增长率的降低可能导致部分解析的涡流太弱。在 C 网格上，对称不稳定性的增长率比在 B 网格上更好（更大），并且随着网格规模减小而向上收敛到正确值。
The effects of horizontal discretization on linear baroclinic and symmetric instabilities are investigated by analyzing the behavior of the hydrostatic Eady problem in ocean models on the B and C grids. On the C grid a spurious baroclinic instability appears at small wavelengths. This instability does not disappear as the grid scale decreases; instead, it simply moves to smaller horizontal scales. The peak growth rate of the spurious instability is independent of the grid scale as the latter decreases. It is equal to c f/Ri where Ri is the balanced Richardson number, f is the Coriolis parameter, and c is a nondimensional constant that depends on the Richardson number. As the Richardson number increases c increases towards an upper bound of approximately 1/2; for large Richardson numbers the spurious instability is faster than the Eady instability. To suppress the spurious instability it is recommended to use fourth-order centered tracer advection along with biharmonic viscosity and diffusion with coefficients (Δ x) 4 f/(32 Ri) or larger where Δ x is the grid scale. On the B grid, the growth rates of baroclinic and symmetric instabilities are too small, and converge upwards towards the correct values as the grid scale decreases; no spurious instabilities are observed. In B grid models at eddy-permitting resolution, the reduced growth rate of baroclinic instability may contribute to partially-resolved eddies being too weak. On the C grid the growth rate of symmetric instability is better (larger) than on the B grid, and converges upwards towards the correct value as the grid scale decreases.
影响因子：
3.2
作者：
Bachman, S. D.;Taylor, J. R.
通讯作者：
Taylor, J. R.