The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide-gap geometry. A three-dimensional disturbance is considered. Linear stability limits in the form of Taylor numbers TaL are computed for the rotation ratios μ, = 0, 0·2, and -0·5 and for values of the axial Reynolds number Re up to 100. Depending on the values of μ and Re, the disturbance which corresponds to TaL can have a toroidal vortex structure or a spiral form. Aluminium-flake flow visualization is used to determine conditions for the onset of a secondary motion and its structure at finite amplitude. The experimental results agree with the predicted values of TaL for μ [ges ] 0, and low Reynolds number. For other cases in which agreement is only fair, apparatus length is shown to be a contributing influence. The comparison between experimental and predicted wave forms shows good agreement in overall trends.

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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.

Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler–Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number, MaE, below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.

Energy-stability theory has been applied to investigate the stability properties of thermocapillary convection in a half-zone model of the float-zone crystal-growth process. An earlier axisymmetric model has been extended to permit nonaxisymmetric disturbances, thus determining sufficient conditions for stability to disturbances of arbitrary amplitude. The results for nonaxisymmetric disturbances are compared with earlier axisymmetric results, with linear-stability results for a geometry with an infinitely long aspect ratio and with stability boundaries from recent laboratory experiments.

The effect of the starting condition on the linear stability properties of circular Couette flow with a time-dependent inner-cylinder motion is investigated. In addition to the WKBJ approach employed previously by Eagles [Proc. R. Soc. London, Ser. A 355, 209 (1977)] for slowly varying flow, an initial-value method is also used. Results are presented for different stability criteria.

The hydrodynamic stability of viscous flow between eccentric rotating cylinders has been studied experimentally. The ratio of the radii of the cylinders was 1 :2; several eccentricities were investigated. In the concentric configuration good agreement was achieved with previous experimental and theoretical work. Results obtained with the cylinders rotating in the same direction show that the effect of eccentricity can be stabilizing or destabilizing depending upon the speed of the outer cylinder and the amount of eccentricity. In the counterrotating case, a new flow phenomenon different from the usual vortex pattern was observed for large eccentricity.