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

Minoru Fujimoto; Kunihiko Uehara; Shinichiro Yanase

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arXiv · 1412.5248

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

Minoru Fujimoto·Kunihiko Uehara·Shinichiro Yanase

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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.

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Minoru Fujimoto, Kunihiko Uehara, Shinichiro Yanase. 2014-12-17. A viscous solution of the spherical vortex to the Navier-Stokes equations. https://arxiv.org/abs/1412.5248

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