Steady Thermal Convection in a Vertical Torus

Abstract

A theoretical study is made on the steady thermal convection of a viscous fluid confined in a vertically oriented thin toroidal loop, which is placed in vertically uniform temperature gradient. The Boussinesq approximation is employed, and first order perturbed fields from steady heat conduction state are examined. Three dimensional cellular flows are found at some critical Rayleigh numbers, which will provide a basic state to understand the bi-directional flow along the loop recently observed in our experiment.