Thermocapillary flow instabilities of medium Prandtl number liquid in rotating annular pools

The linear stability of thermocapillary flow for a medium Prandtl number liquid (Pr = 6.7) is investigated in the annular pools rotating along counterclockwise direction. The neutral Reynolds numbers for the incipience of instabilities are determined by linear stability analysis and the underlying mechanisms are analyzed by energy budgets. Four types of oscillatory instabilities are predicted for different aspect ratios over a wide range of Taylor number. The energy budgets reveal that all the instabilities are basically driven by the hydrothermal wave instability mechanism of moderately large-Prandtl-number liquid. The pool rotation influences the basic flow and enables the disturbances to receive energy in different ways. When the system rotation is initiated, the axisymmetric steady thermocapillary flow becomes unstable typically by a hydrothermal wave instability (type I) for all aspect ratios. The slow rotation destabilizes the basic flow whereas the fast rotation stabilizes it when the Taylor number exceeds a certain threshold value. For large Taylor numbers, two types of flow instabilities (types II and III) occur in sequence with increasing aspect ratio. While type IV arises in a range of Taylor number between those of the type I and type II for the layer of A = 0.25. The critical Reynolds numbers for the onset of the later three oscillatory bifurcations all increase with increasing Taylor number.