Rossby-Haurwitz waves on the sphere $S^2$ form a set of exact time-dependent solutions to the Euler equations of hydrodynamics and generate a family of non-stationary geodesics of the $L^2$ metric in the volume preserving diffeomorphism group of $S^2$. Restricting to a particular subset of Rossby-Haurwitz waves, this article shows that under certain conditions on the physical characteristics of the waves each corresponding geodesic contains conjugate points. In addition, a physical interpretation of conjugate points is given and links the result to the stability analysis of meteorological Rossby-Haurwitz waves.

中文翻译：

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共轭点，单位为 Dμs(S2)

球面上的罗斯比-豪维茨波 ${秒}^2$ 形成流体动力学欧拉方程的一组精确的时间相关解，并生成一系列非平稳测地线 ${升}^2$ 体积保持微分同胚群中的度量 ${秒}^2$. 限于 Rossby-Haurwitz 波的一个特定子集，本文表明在波的物理特性的特定条件下，每个对应的测地线都包含共轭点。此外，还给出了共轭点的物理解释，并将结果与​​气象罗斯比-豪维茨波的稳定性分析联系起来。