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 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.