A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

Several means for visualizing large-scale vortex structure in a turbulent mixing layer are proposed. Most of the observations are recorded along the low-speed side of the mixing layer, external to the rotational portion of the flow. Conventional correlation measurements in both the streamwise and spanwise directions indicate that the vortex structure becomes independent of the downstream coordinate in a non-dimensional distance of order λx/θi = 300–400, where $\lambda = \Delta U/2\overline{U}$ is the speed ratio and θi is the initial integral thickness. Simultaneous hot-wire measurements at 12 spanwise positions allow computer reconstruction of the velocity field as a function of span and time. These visualizations show the vortex structures to be primarily aligned across the span of the flow, but to contain irregularities. Spanwise correlation lengths are of the order of 3–5δω (δω is the local vorticity thickness). However, the large vortices typically have lengths of order 20δω when the irregularities along the span are ignored.

Results of laboratory experiments are used to determine the morphology and the ascent rate of growing buoyant plumes in a homogeneous, viscous fluid. The plumes were formed by injecting a glucose solution through a small orifice into another glucose solution of different density. Two classes of creeping (low-Reynolds-number) plumes are investigated: (i) diapiric plumes, for which the plume viscosity is approximately equal to the ambient-fluid viscosity, and (ii) cavity plumes, for which the plume fluid is much less viscous than the ambient fluid. Fully developed diapirs consist of a tapered cylindrical stem capped by a mushroom-shaped vortex at its leading edge. Fully developed cavity plumes consist of a nearly spherical chamber connected to the source by a narrow umbilical conduit. It is observed that the ascent velocity of cavity plumes increases with time as t⅖. The ascent velocity of diapirs is found to be proportional to the terminal velocity of a cylinder moving parallel to its axis. The presence of pre-existing conduits alters the morphology of cavity plumes and greatly increases their ascent rate. Fossil conduits act as plume guides by offering low-resistance ascent paths. Finally, a series of experiments have been made on the interaction between cavity plumes and a large-scale background circulation. A low-viscosity plume generated by a source towed steadily through a highly viscous fluid breaks into a chain of regularly spaced, individual cavities, as first demonstrated by Skilbeck & Whitehead. The cavities ascend as an inclined linear array of Stokes droplets. Dimensional analysis is used to derive scaling laws for the cavity volumes and their replication rate in terms of the source parameters and the tow speed. The qualitative results from these experiments generally lend support to the hypothesis that buoyant plumes in the Earth's mantle are the source of hot-spot volcanism. In particular the experiments suggest an explanation for the observation that hot spots remain nearly fixed in the presence of mantle convection.