Numerical investigation of the convective flow in the toroidal gap

A numerical investigation of the convective flow in the toroidal gap is presented. A new formulation of the incompressible Navier–Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation [Weinen and Liu in Commun Math Sci 1(2):317–332, 2003] has been used. The gauge freedom allows simple boundary conditions to be formulated for the auxiliary field, as well as the gauge field. The gauge field eliminates the pressure distribution in the Navier–Stokes equation. The influence of the geometric parameters and the Prandtl number is discussed.