Instability mechanisms for thermocapillary flow in an annular pool heated from inner wall

The linear stability analysis of thermocapillary flow in an annular pool heated from inner wall was performed by using spectral element method. The physical instability mechanisms for different Prandtl numbers (Pr) ranging from 0.001 to 1.4 were studied by energy analysis under critical mode. We observed three instability types: (i) the Hopf (oscillatory) bifurcation with wavenumber k = 18 for Pr < 0.02, and the corresponding neutral mode is amplified due to the basic shear flow; (ii) the stationary instability with k = 3 or k = 2 for 0.02 < Pr < 0.6; (iii) the Hopf bifurcation again with k = 3 for 0.6 < Pr < 1.4. In both Prandtl number ranges of 0.02 < Pr < 0.6 and 0.6 < Pr < 1.4, thermocapillary force induced by the disturbance temperature field drives primarily the flow instability.