Exact steady-state solutions of 3D toroidal flows and their stability

The purpose of the article is three-fold. The first is to get the Navier–Stokes equations in the toroidal coordinates by the methods of Riemannian geometry, which govern the motion of flows confined in a nested tori with inner torus rotating at a constant horizontal angular velocity. The second is t...

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Bibliographic Details
Published in:Journal of geometry and physics 2018-10, Vol.132, p.205-221
Main Authors: Yang, Jiayan, Wang, Quan, Liu, Ruikuan
Format: Article
Language:English
Subjects:
Continuous and catastrophic transition
Implicit function theorem
Navier–Stokes equations
Riemannian geometry method
Toroidal coordinates
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Summary:The purpose of the article is three-fold. The first is to get the Navier–Stokes equations in the toroidal coordinates by the methods of Riemannian geometry, which govern the motion of flows confined in a nested tori with inner torus rotating at a constant horizontal angular velocity. The second is to obtain the corresponding steady-state solutions by using the Implicit Function Theorem and iterative techniques. The last objective is to show the linear stability of the derived steady-states.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2018.06.006