[论文解读] Effects of Horizontal Discretization on Triangular and Hexagonal Grids on Linear Baroclinic and Symmetric Instabilities

Steffen Maaß, Sergey Danilov|arXiv (Cornell University)|Jan 7, 2026

Oceanographic and Atmospheric Processes被引用 0

一句话总结

论文分析在三角形和六边形网格上的水平离散化（B 和 C 摆放）如何影响线性热成屈和对称不稳定性，揭示与网格几何相关的伪模态，并指出需要调整粘度/扩散以减轻它们。

ABSTRACT

As global ocean general circulation models are run at eddy-permitting resolutions, reproducing accurate growth rates of baroclinic instabilities is a major concern when choosing a discretization of the equations of motion. From this viewpoint, we analyze discretizations on triangular and hexagonal grids with different types of variable staggering used in several ocean circulation models. By extending the linear baroclinic instability analysis in the Eady configuration to discretizations on more complex grids, several numerical subtleties are revealed. In comparison to discretizations on quadrilateral grids, the analyzed discretizations are less robust against unstable spurious modes, partly created by the mesh geometry. Some of the subtleties arise because spurious modes on staggered triangular and hexagonal grids do not adhere to Galilean invariance. As a consequence, their growth rates demonstrate a dependence on the alignment between the background flow and the grid, as well as the strength of a uniform background flow. The interactions with spurious modes become more significant on the axis of symmetric instabilities where the physical and spurious branches of instability are more difficult to separate in wavenumber space. Our analysis shows that in most cases moderate biharmonic viscosity and diffusion suppress spurious branches. However, one needs to carefully calibrate the viscosity and diffusivity parameters for each of the considered discretizations in order to achieve this.

研究动机与目标

• 评估在 Eady 配置中，三角形和六边形网格离散化（B 和 C 摆放）如何再现线性热成屈和对称不稳定性。
• 识别由网格几何和摆放差异引起的数值细微差别及伪模态。
• 评估粘度和扩散在不同离散化下抑制伪不稳定分支的有效性。

提出的方法

• 将线性热成屈不稳定性分析（Eady 问题）扩展到三角形和六边形网格。
• 为 B 和 C 网格在非结构化网格上开发离散水平算子和傅里叶符号。
• 比较对流格式（FDV、FDCRE、AVI、ASC）及其对稳定性和伪模态的影响。
• 结合摆放网格考虑和重建方案，分析热浮力的输运。
• 提供补充笔记本，包含六边形 C 网格和三角 A 网格的傅里叶符号分析以示完整性。

实验结果

研究问题

• RQ1 三角形 B- 和 C 网格离散化在 Eady 配置中如何再现热成屈和对称不稳定性的增长率？
• RQ2 由于网格几何和摆放差异产生的伪模态是什么，它们如何依赖背景流的对齐？
• RQ3 粘度和扩散在多大程度上抑制不同离散化中的伪不稳定分支？
• RQ4 不同的水平动量和浮力离散化如何影响伪模态的存在和行为？

主要发现

• 伪模态在错位的三角形和六边形网格上出现，原因在于速度和标量自由度的不平衡及网格几何。
• 伪模态可能依赖于背景流与网格的对齐以及均匀背景流的强度，表明某些方案中存在伽利略不变性损失。
• 中等强度的双拉姆粘性和扩散通常在各离散化下抑制伪不稳定分支，但需要针对每种离散化进行标定。
• 某些对流格式（如 FDCRE、ASC）能够改善物理分支的准确性，但可能引入相反方向的伪几何模态。
• 研究表明，伪模态的相互作用在对称不稳定轴附近更显著，此时物理分支和伪分支在波数空间中重叠。
• A 网格（三角形）布置不易出现伪不稳定，而六边形以及三角 B/C 网格需要谨慎处理。