Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges

The dynamics of thermocapillary hows in differentially heated cylindrical l iquid bridges is investigated numerically using a mixed finite volume/pseud o-spectral method to solve the Navier-Stokes equations in the Boussinesq ap proximation. For large Prandtl numbers (Pr = 4 and 7) and sufficiently high Reynolds numbers, the axisymmetric basic flow is unstable to three-dimensi onal hydrothermal waves. Finite-amplitude azimuthally standing waves are fo und to decay to travelling waves. Close to the critical Reynolds number, th e former may persist for long times. Representative results are explained b y computing the coefficients in the Ginzburg-Landau equations for the nonli near evolution of these waves for a specific set of parameters. We investig ate the nonlinear phenomena characteristic of standing and pure travelling waves, including azimuthal mean flow and time-dependent convective heat tra nsport. For Pr much less than 1 the first transition from the two-dimension al basic flow to the three-dimensional stationary flow is inertial in natur e. Particular attention is paid to the secondary transition leading to osci llatory three-dimensional flow, and this mechanism is likewise independent of Pr. The spatial, and temporal structure of the perturbation flow is anal ysed in detail and an instability mechanism is proposed based on energy bal ance calculations and the vorticity distribution.