Effect of temperature gradients on axial vortex breakdown

In this study, we do a direct numerical simulation to understand the effect of temperture gradient on an axial vortex breakdown. 
This is achieved by rotating the top lid of a cylinder which is heated at the bottom and cooled at the top. 
We study the dynamics of the confined fluid inside the cylinder, at different rotational rates of the lid and heating of the end walls. 
The problem finds application in natural flows where fluid rotates over heated surface as in hurricanes, as well as in engineering problems involving breakdown bubbles which used for aerodynamic stabilization of flames in a premixed swirl combustor.
A three dimensional Navier Stokes simulation of such a problem is less explored, that we undertake here. 
The initially swirl flow establishes a breakdown bubble as rotational rate is increased, and gets modified to generate non-axisymmetry in flow, when temperature gradients are applied.
Also, we propose a simple analytical model, which relies on inviscid nature of breakdown bubble phennomena, to capture the stagnation points at the axis. 
This confirms that, at increased rotational rates, spatial localization of azimuthal vorticity induces negative velocity causing vortex breakdown bubble.