Abstract
AbstractA cylindrical volume of fluid, with a free surface on top, is heated by a parabolic heat flux from above. Two physical effects drive a flow: thermocapillary effects due to free‐surface temperature gradients introduced by the non‐uniform heat flux and buoyancy forces due to gravity. The basic axisymmetric flow is computed by finite volumes and its stability is investigated by a linear‐stability analysis. It is found that the critical stability boundaries and modes are similar to those known from the half‐zone model of crystal growth. For low Prandtl numbers the critical mode is steady and three‐dimensional. We find an asymptotic critical value in the limit of vanishing Prandtl number. For increasing Prandtl number the critical Reynolds number increases. Near unit Prandtl number no threshold could be found with the present computational limitations. For Prandtl numbers larger than unity, the critical mode is oscillatory and the critical Reynolds number decreases with the Prandtl number. We present evidence that the low‐ and high‐Prandtl‐number instabilities are essentially centrifugal respectively due to the hydrothermal‐wave mechanism. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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