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.