An experimental study of the origin of oblique vortex shedding in the laminar wake of circular cylinders was conducted in the range of Reynolds numbers from 40 to 160. Two transverse circular cylinders were positioned upstream of the main shedding cylinder to control the angle of shedding from the main cylinder. The respective distances between each transverse cylinder and the main cylinder were used to induce oblique shedding of different angles, curved shedding, as well as parallel shedding. Measurements of the mean static pressure distribution in the base region of the cylinder and of the mean spanwise component of the velocity in the wake were taken. These measurements revealed that a non-symmetric pressure distribution, which induced a spanwise flow in the base region of the cylinder, was responsible for the oblique shedding. By using a simple model based on the ratio of the streamwise to the spanwise vorticity components, the angle of shedding was predicted within 2° of the value measured from flow visualization. The vorticity was simply evaluated from the spanwise and streamwise velocity profiles of oblique vortex streets obtained with the LDV measurement technique. Parallel vortex shedding showed a symmetric pressure distribution with zero spanwise component of the velocity and zero cross-shear in the cylinder base. It was shown that parallel vortex shedding results in a continuous Strouhal–Reynolds number curve.

The transition from steady to oscillatory three-dimensional convection in a cube of saturated porous material is calculated to occur at Rayleigh number R = 584 due to seven pairs of thermal blobs which circulate around the cube. This travelling wave instability is shown to be closely related, first as regards structural characteristics and then as regards mechanism of instability, to an analogous instability in two dimensions. The correspondence with the two-dimensional flow is established via a correspondence with a nonlinear base flow in a box of square planform of a different aspect ratio (l/√2) and ultimately derives from the symmetries of the base flow in the cube.

The influence of uniform flow acceleration on the stability and the characteristics of circular-cylinder wakes over a Reynolds-number range, 20 < R < 330, was investigated. Experiments were performed to examine the temporal evolution of the wake before, during, and after the onset of the wake instability. We have demonstrated in several ways that the wake is stabilized by flow acceleration: (i) the onset of the wake instability occurs at larger Reynolds numbers than in the steady flow case, (ii) the closed wake develops to states that would be unstable in a steady flow, and (iii) once vortex shedding does occur there is a reduction in instantaneous Strouhal number. We have also examined the temporal growth rate of the wake instability and find that it is directly proportional to the applied flow acceleration. Physical mechanisms are proposed to describe the experimental observations.

Motivated by the recent work of Bajer & Moffatt (1990), we investigate the kinematics of bounded steady Stokes flows. Specifically, we consider the streamlines inside a neutrally buoyant spherical drop immersed in a general linear flow. The Eulerian velocity field internal to the drop, known analytically, is a cubic function of position. For a wide range of parameters the internal streamlines, hence the fluid particle paths, may wander chaotically. Typical Poincaré sections show both ordered and chaotic regions. The extent and existence of chaotic wandering is related to (i) the orientation of the vorticity vector relative to the principal axes of strain of the undisturbed flow and (ii) the magnitude of the vorticity relative to the magnitude of the rate-of-strain tensor. In the limit of small vorticity, we use the method of averaging to predict the size of the dominant island region. This yields the critical orientation of the vorticity vector at which this dominant island disappears so that particle paths fill almost the entire Poincaré section. The problem studied here appears to be one of the simplest, physically realizable, bounded steady Stokes flows which produces chaotic streamlines.

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Görtler and crossflow vortices. The change in structure of Görtler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Görtler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Görtler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Görtler mechanism is probably not present for typical angles of sweep of about 20°.

Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.

Eckart's (1952) second-order, self-adjoint partial differential equation for the free-surface displacement of monochromatic gravity waves in water of variable depth h is derived from a variational formulation by approximating the vertical variation of the velocity potential in the average Lagrangian by that for deep-water waves. It is compared with the ‘mild-slope equation’, which also is second order and self-adjoint and may be obtained by approximating the vertical variation in the average Lagrangian by that for uniform, finite depth. The errors in these approximations vanish for either κh ↓ 0 or κh ↑ ∞ (κ ≡ ω2/g). Both approximations are applied to slowly modulated wavetrains, following Whitham's (1974) formulation for uniform depth. Both conserve wave action; the mild-slope approximation conserves wave energy, but Eckart's approximation does not (except for uniform depth). The two approximations are compared through the calculation of reflection from a gently sloping beach and of edge-wave eigenvalues for a uniform slope (not necessarily small). Eckart's approximation is inferior to the mild-slope approximation for the amplitude in the reflection problem, but it is superior in the edge-wave problem, for which it provides an analytical approximation that is exact for the dominant mode and in error by less than 1.6% for all higher modes within the range of admissible slopes. In contrast, the mild-slope approximation requires numerical integration (Smith & Sprinks 1975) and differs significantly from the exact result for the dominant mode for large slopes.