This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

Stokes flow in a two-dimensional cavity of rectangular section, induced by the motion of one of the walls, is considered. A direct, efficient calculational procedure, based on an eigenfunction expansion, is used to study the eddy structure in the cavity. It is shown that some of the results of earlier studies are quantitatively in error. More importantly, two interesting questions, namely the extent of the symmetry of the corner eddies and their relationship to the large-eddy structure are settled. By carefully examining the rather sudden change in the main eddy structure for cavities of depth around 1.629, it is shown that the main eddies are formed by the merger of the primary corner eddies; the secondary corner eddies then become the primary corner eddies and so on. Thus, in the evolution of the large-eddy structure the corner eddies, in some sense, play the role of progenitors. This explicit prediction should be experimentally verifiable.

We consider Stokes flow in a cylindrical container of circular section induced by the uniform translatory motion of one of the endwalls. This flow field is of interest because it is possible to get reliable analytical descriptions of important three-dimensional structures such as the primary and corner eddies. It is shown, using a result of Tran-Cong & Blake, that separable solutions exist which can be combined to yield vector eigenfunctions that satisfy the sidewall boundary conditions provided the eigenvalues satisfy the transcendental equationformula here

We have measured the kinematic viscosity of glycerol-water mixtures, for glycerol mass fractions ranging from 0 to 1, in the temperature range 10-50 °C. The measurements were made by using a series of Ubbelohde viscometers. Apart from comprehensiveness and comparative accuracy the present measurements expose serious errors in the limited data that were earlier available on such mixtures. It is shown that all the data can be reasonably represented by the empirical correlation (In ν m - In ν w )/(In ν g - In ν w ) = x g [1 + (1 - x g ) { a + bx g + cx g 2 }], where ν w , v g and ν m are the kinematic viscosities of water, glycerol and the mixture respectively and x g is the mass fraction of glycerol in the mixture. The constants a, b and c are tabulated in the paper as functions of temperature. This correlation can now be used at a given temperature to tailor make a mixture of prescribed kinematic viscosity. While this paper is addressed, principally, to fluid dynamicists these results should be of interest to physicists studying the liquid state and physical chemists interested in mixtures.

Consider a cylindrical container of circular section filled with a viscous fluid. We consider flow in such a cylinder driven by the motion of flat belts across the partially open end walls of the container. The flow field is determined by the use of a vector eigenfunction expansion. The critical points that are exhibited in the plane of symmetry include elliptic points, foci, and saddles. As the parameters are varied one can have bifurcations in which one type of critical point bifurcates to a collection of others. An example of a limiting surface is also demonstrated. Since the flow fields considered have little symmetry, the three-dimensional streamlines are for the most part not closed. As a consequence the flow fields tend to globalize structures that would otherwise have been isolated. This feature can have important consequences for mixing.