Effects of Prandtl number and a new instability mode in a plane thermal plume

The effect of Prandtl number on the linear stability of a plane thermal plume is analyzed under quasi-parallel approximation. At large Prandtl numbers ($Pr>100$), we found that there is an additional unstable loop whose size increases with increasing $Pr$. The origin of this new instability mode is shown to be tied to the coupling of the momentum and thermal perturbation equations. Analyses of the perturbation kinetic energy and thermal energy suggest that the buoyancy force is the main source of perturbation energy at high Prandtl numbers that drives this instability.