2019/07/19 by Taito Tauchi, Tauchi, Taito, Tsuyoshi Yoneda +1 · 1 citation
Engineering · Mathematics · #35Q35 (Primary) #58B20(Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Geophysics (physics.geo-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1907.08365
openalex publication_date 2019/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiolek (1996) formulated a differential-geometric criterion (we call M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) satisfies M-criterion if the background manifold is a sphere, on the other hand, there are zonal flows satisfy M-criterion if the background manifold is an ellipsoid (even it is sufficiently close to the sphere). The conjugate point is created by the fully nonlinear effect of the inviscid fluid flow with differential geometric mechanism.