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Conjugate points in Dμs(S2)
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-09-08 , DOI: 10.1016/j.geomphys.2021.104369
J. Benn

Rossby-Haurwitz waves on the sphere S2 form a set of exact time-dependent solutions to the Euler equations of hydrodynamics and generate a family of non-stationary geodesics of the L2 metric in the volume preserving diffeomorphism group of S2. 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:

共轭点,单位为 Dμs(S2)

球面上的罗斯比-豪维茨波 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 2 体积保持微分同胚群中的度量 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。

更新日期:2021-09-16
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