The results given by Brenner & Cox (1963) for the resistance of a particle of arbitrary shape in translation at small Reynolds numbers are generalized. Thus we consider here a single particle of arbitrary shape moving with both translation and rotation in an infinite fluid, the Reynolds number R of the fluid motion being assumed small. With the additional assumption that the motion is steady with respect to some inertial frame of reference, we calculate both the force and couple on the body as an expansion in the Reynolds number to O(R2 In R). This force and couple are expressed entirely in terms of various Stokes flows for the given body in rotation or translation.

A discussion is given of the form taken by the formulae for the force and couple for cases in which the body possesses symmetry properties. Quantitative results are obtained for both a spheroid and a dumb-bell-shaped body in pure translation and also for a translating rotating sphere and for a dumb-bell-shaped body in pure rotation.

The application of the general results to ‘quasi-steady’ problems is considered, with particular reference to a freely falling spheroid (of small eccentricity) which is shown to orientate itself so that it is broad-side on to its direction of motion.

Finally the general results are compared with those that would be obtained by the use of the Oseen equations. By consideration of a particular example it is shown that the Oseen equations do not in general give the correct value of the force on the body to O(R).

Measurements of cavities behind disks in a water tunnel show that at high enough speeds the cavity pressure is not more than 30–40% higher than water-vapour pressure, even when at atmospheric pressure the tunnel water is nearly saturated with air. No other hard conclusions can be drawn from the investigations, which showed many puzzling features, discussed below. It is hoped, however, that the qualitative discussion may prove useful to theoreticians who may seek to improve existing mathematical models of cavitation by taking a more realistic account of the physics of the flow.

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.

Similarity solutions in which the vorticity decays algebraically towards the outer limit of the viscous layer are shown to be possible limit solutions of the full boundary-layer equations with exponential decay. The discussion is illustrated by consideration of a mainstream applicable to viscous flow in a cone.

For fully-developed turbulent flow in straight channels of non-circular cross-section, there exists a transverse mean flow superimposed upon the axial mean flow. This transverse flow, commonly known as secondary flow, interacts with the axial mean flow and turbulence structure in a complex manner. In this paper several heretofore unexplored aspects of this type of secondary flow are discussed on the basis of results of an extensive experimental programme which was conducted for steady, incompressible, fully-developed turbulent air flow in both square and rectangular channels. Specifically, the following aspects are examined: (a) the Reynolds-number effect on secondary flow, (b) the directional characteristics of local wall shear stress, (c) the orientation of Reynolds-stress principal planes in a plane normal to the axial flow direction, and (d) the Reynolds equation along a secondary-flow streamline.

Within the Reynolds-number range of the investigation, the results indicate that secondary-flow velocities, when non-dimensionalized with either the bulk velocity or the axial mean-flow velocity at the channel centreline, decrease for an increase in Reynolds number. Also, the greatest skewness of local wall shear-stress vectors is shown to occur in the near vicinity of corners where secondary flow is maximum. In addition, it is shown that in planes normal to the axial flow direction, traces of Reynolds stress principal planes are not tangent and normal to lines of constant axial mean-flow velocity. This behaviour is in contrast to that for less complicated turbulent flows, for example, two-dimensional channel flow or circular-pipe flow where such traces are always tangent and normal to lines of constant axial mean-flow velocity in accordance with symmetry considerations. Finally, through experimental evaluation of terms in a momentum balance along a typical secondary-flow streamline, it is shown that secondary flow is the result of small differences in magnitude of opposing forces exerted by the Reynolds stresses and static pressure gradients in planes normal to the axial flow direction.

This paper presents a discussion of some aspects of the linear stability problem for the asymptotic suction profile. An exact solution of the inviscid equation is first obtained in terms of the usual hypergeometric function and its analytical continuation. This exact solution provides both a corrected version of an earlier treatment by Freeman and an independent check on the more general method suggested for solving the inviscid equation numerically. Various approximations to the characteristic equation, and hence to the curve of neutral stability, are then considered. In particular, it is found that, in a consistent asymptotic treatment of the related adjoint problem, at least one viscous correction to the singular inviscid solution must be considered. Based on the present results for the adjoint problem, it is suggested that Tollmien's original treatment of the viscous corrections must be slightly modified.

The effect of an adverse pressure gradient on the stability of a laminar boundary layer is considered in the limiting case when the skin friction at the wall vanishes, i.e. when U′(0) = 0. Such flows are not absolutely unstable as might have been expected but have a minimum critical Reynolds number of the order of 25. General results are given for the asymptotic behaviour of both the upper and lower branches of the neutral curve and a complete neutral curve is obtained for Pohlhausen's simple fourth-degree polynomial profile at separation.

The terminal velocity of rise of small, distorted gas bubbles in a liquid of small viscosity is calculated. Small viscosity means that the dimensionless group gμ4/ρT3 where g is the acceleration of gravity, μ the viscosity, ρ the density and T the surface tension, is less than 10−8. It is assumed—and the numerical accuracy of the assumption is discussed—that the distorted bubbles are oblate ellipsoids of revolution. The drag coefficient is found by extending the theory given recently (Moore 1963) for the boundary layer on a spherical gas bubble. The results are in reasonable quantitative agreement with the experimental data.

The development of a turbulent boundary layer in a strong adverse pressure gradient can be described by the two-layer model proposed by Stratford (1959), in which the outer part of the flow is assumed to be unmodified by the pressure-rise and the inner part described by two local parameters, the surface stress and the pressure gradient. The description suggests that the modification of the original flow is in some sense self-preserving, and it is shown here that self-preserving development of the modification is consistent with the Reynolds equations of turbulent flow in particular pressure distributions. For these distributions, the predictions of the two-layer model are confirmed without any need to make the sharp and arbitrary distinction between the two parts of the boundary layer.

An investigation is made into the propagation of a one-dimensional combustion wave, which consists of a flame front and a precursor shock wave which pass down a tube closed at one end, in the presence of a transverse magnetic field in the undisturbed gas at rest. The shock wave is assumed to be of sufficient strength to ionize completely the initially non-electrically-conducting gas and the conditions at the flame front are taken to satisfy the Chapman–Jouguet condition. Details of the solution are compared with the corresponding results for ordinary gasdynamic deflagration.

Theoretical and experimental investigations are described of the linearized wave equation of supersonic flow with a single relaxation process. Firing-range experiments using a known model gas mixture with a single relaxation process are discussed. Qualitatively, it is shown that weak conical and spherical waves decay as predicted by theory. In addition, this decay can be determined quantitatively for conical disturbances; and, satisfactory agreement with theory is found. For application to unknown relaxation processes, it is suggested that observation of the damping of weak waves provides an additional tool for the study of fast rate processes.

The first in a new series of European research conferences in mechanics was held in Berlin on 5 and 6 April 1965. The subject was the Coanda effect, or boundary layers and jets on highly curved walls. Participation was restricted to about 40 people, invited on the basis of their active interest in the subject. These Colloquia are intended to have an informal, workshop-like, character, and formal papers are not normally available, nor will any full proceedings be published. The first author was the chairman of the Colloquium. The following account of the scientific developments of the Colloquium has been prepared to make them widely available. The references quoted give further details of the work discussed at the Colloquium and of related previous work.