The primary instability of axisymmetric steady thermocapillary flow in a cylindrical liquid bridge with non-deformable free surface is calculated by a mixed Chebychev-finite difference method. For unit aspect ratio the most dangerous mode has an azimuthal wavenumber m=2. The physical instability mechanisms are studied by analyzing the linear energy balance of the neutral mode. If the Prandtl number is small (Pr≪1), the bifurcation is stationary. The associated neutral mode is amplified in the shear layer close to the free surface. For large Prandtl number (Pr=4), the basic state becomes linearly unstable to a pair of hydrothermal waves propagating nearly azimuthally. Both mechanisms are compared with those previously proposed in the literature.
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Wanschura et al. (1995) studied this question.
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