ALBERT

Description: The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results. © 1971, Cambridge University Press. All rights reserved.

Description: The stability of viscous time-dependent rotational Couette flow, induced by an impulsively started inner cylinder was experimentally investigated. The ratio of the radius of the inner cylinder to that of the outer cylinder was [formula omitted]. The space between the cylinders was filled with distilled water. The time-dependent instabilities were observed by means of dye injection. They appeared as a series of disks more or less evenly spaced along the inner cylinder. The spacing and growth of these instabilities were recorded using a motion picture camera. From the motion pictures the critical time (which is the time from the impulsive start to the first onset of instability) and spacing of the instabilities were experimentally determined, and a marginal stability curve (Reynolds number versus critical time) was constructed. © 1970, Cambridge University Press. All rights reserved.