This paper describes a method for examining the collapse of arrays of cavities using high-speed photography and the results show a variety of different collapse mechanisms. A two-dimensional impact geometry is used to enable processes occurring inside the cavities such as jet motion, as well as the movement of the liquid around the cavities, to be observed. The cavity arrangements are produced by first casting water/gelatine sheets and then forming circular holes, or other desired shapes, in the gelatine layer. The gelatine layer is placed between two thick glass blocks and the array of cavities is then collapsed by a shock wave, visualized using schlieren photography and produced from an impacting projectile. A major advantage of the technique is that cavity size, shape, spacing and number can be accurately controlled. Furthermore, the shape of the shock wave and also its orientation relative to the cavities can be varied. The results are compared with proposed interaction mechanisms for the collapse of pairs of cavities, rows of cavities and clusters of cavities. Shocks of kbar (0.1 GPa) strength produced jets of c. 400 m s−1 velocity in millimetre-sized cavities. In closely-spaced cavities multiple jets were observed. With cavity clusters, the collapse proceeded step by step with pressure waves from one collapsed row then collapsing the next row of cavities. With some geometries this leads to pressure amplification. Jet production by the shock collapse of cavities is suggested as a major mechanism for cavitation damage.

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

Numerical solutions are presented for steady incompressible flow past a sphere. At high Reynolds numbers (results are presented up to R = 5000), the wake is found to resemble a Hill's spherical vortex.

Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Control of vortex formation from a circular cylinder by a long plate in its wake is examined over the Reynolds number range 140 < Re < 3600. There are two basic flow regimes: a pre-vortex formation regime, in which the plate precludes formation of a large-scale vortex upstream of the tip of the plate; and a post-vortex formation regime in which one or more large-scale vortices are formed upstream of the edge. The unsteady pressure loading at the tip of the plate increases by over an order of magnitude during transition from the pre- to post-vortex formation regime. If the plate is located near the cylinder, it is possible to more than double the vortex formation length, relative to the case of the free wake. Moreover, these observations suggest that: there is a minimum streamwise lengthscale for development of the absolute instability of the near wake and thereby the large-scale vortex; and the vortex formation length may also be influenced by the downstream vorticity dynamics. When the plate is located downstream of the initially formed vortex, effective control is possible when the near-wake fluctuation level and mean base pressure of the corresponding free (non-impinging) wake are sufficiently small. This occurs in the low and moderate subcritical regimes; the substantial control by the wake-plate interaction in this range of Reynolds number implies low strength of the absolute instability of the near wake. However, in the pure von Kármán regime, selfcontrol of the near wake dominates that imposed by the wake-edge interaction, suggesting a strong absolute instability of the near wake.

The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x’, t) given the velocity and the deformation tensor at a point x: 〈u(x’, t)|u(x, t), d(x, t)〉. By means of linear mean-square stochastic estimation, 〈u’|u, d〉 is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the ‘legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively.

The equation governing the joint probability density function of fu,d (u, d) is derived. It is shown that this equation contains 〈u’/u, d〉 and that the equations for second-order closure can be derived from it. Closure requires approximation of 〈u’/u, d〉.

The problem considered is the determination of the mass of the drops which break away when a viscous liquid drips slowly out of a narrow vertical tube. A simple one-dimensional theory of the unsteady extension of a viscous thread under its own weight is given, which holds when viscosity, capillarity and gravity are important but inertia is negligible. A comparison with experiment is given. There are several systematic errors, the most important of which are associated with detailed behaviour at the pipe exit where die-swell and wetting are difficult to assess. With due allowance for these errors, agreement is fairly good.

The IUTAM Symposium Fundamental Aspects of Vortex Motion was held in Tokyo, Japan, from 31 August to 4 September 1987. We present an account of the technical sessions of that meeting. The main goals of this report are (i) to provide a widely accessible record of the four-and-one-half day meeting; (ii) to identify important new developments in the field of vortex dynamics of potential interest to a larger audience than the invited attendees; and (iii) to attempt some overview comments with the wisdom of hindsight that may be useful as a guide to specific papers in the proceedings and other current literature.