Stability study of the floating zone with respect to the Prandtl number value

Abstract

Thermocapillary convection in a laterally heated liquid bridge is studied numerically, using a Chebyshev spectral method. The stability of the axisymmetric basic state, with respect to 3D perturbations, is characterized over a large range of Prandtl number values (Pr∊[10−3,102]), thanks to the choice of a sufficiently sharp regularizing function of the vorticity singularities. Criteria are established to ensure the compatibility of this function with mass conservation, and to choose a correct model of the lateral heat flux in order to reach a spectral convergence of the results. First 3D nonlinear spectral computations are presented.