A viscous solution of the spherical vortex to the Navier-Stokes equations

2014/12/17 by Minoru Fujimoto, Fujimoto, Minoru, Kunihiko Uehara +3
Earth and Planetary Sciences · Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #General Physics (physics.gen-ph) #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.1412.5248

openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the Hill's spherical vortex, which is an exact solution to the Euler equation, and manage the solution to satisfy the incompressible Navier-Stokes(INS) equations with a viscous term. Once we get a viscous solution to the INS equations, we will be able to analyze the flows with discontinuities in vorticity. In the same procedure, we also present a time developing exact solution to the INS equations, which has a rotation on the axis besides the Hill's vortex.

Related

• Hill's Spherical Vortex in a Rotating Fluid
• On the Hill's Spherical Vortex in Fluid and Plasma, its Generalization, and Stability
• Exact solutions of fluid equations on a sphere
• Stability of Hill's spherical vortex
• Vortex solutions of the generalized Beltrami flows to the incompressible Euler equations