Instabilities in a Laterally Heated Full-zone with a Large Aspect Ratio

Abstract

The stability of a laterally heated full -zone (FZ) to three -dimensional disturbances is investigated for aspect ratios (length/diameter) ranging from 2 to 20 and for a Prandtl number of 0.001. Over this range of aspect ratio, the linear stability analysis predicts a transition from steady axisy mmetric flow to steady three -dimensional flow with an azimuthal wave number of one. As the aspect ratio increases, the critical parameters converge for modes with both the same and opposite symmetry as the base flow. The results are compared to the linear stability of the infinite -length cylindrical bridge with a constant temperature gradient in the axial direction and return flow. For small Prandtl numbers, the infinite zone (IZ) is most susceptible to instabilities involving traveling hydrothermal waves with an azimuthal wave number of one and with an axial wave number which varies with Prandtl number. We find that the long but finite FZ never displays the behavior of the infinite zone because end effects play a key role in the instability mechanism.