Instabilities of thermocapillary convection in a half-zone at intermediate Prandtl numbers

Abstract

The stability of thermocapillary convection inside a cylindrical liquid bridge is studied using both a direct numerical simulation of the three-dimensional problem and linear stability analysis of the axisymmetric basic state. Previously this has been studied extensively for low and high Prandtl numbers. However, the intermediate range of Prandtl numbers between approximately 0.07 and 0.8 which joins the low and high ranges is quite complicated and has not been studied to the same extent. One striking feature is that the axisymmetric base state is much more stable in this intermediate range than at high or low Prandtl numbers. We identify four different oscillatory modes in this range, which have different qualitative features. Direct numerical simulations have been carried out for representative parameter values, and show that the bifurcations are supercritical.