Linear-stability theory of thermocapillary convection in a model of the float-zone crystal-growth process

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities are nonseparable partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases; they complement recent calculations of the corresponding energy-stability limits.