Some simple similarity solutions are presented for the flow of a viscous fluid near a sharp corner between two planes on which a variety of boundary conditions may be imposed. The general flow near a corner between plane boundaries at rest is then considered, and it is shown that when either or both of the boundaries is a rigid wall and when the angle between the planes is less than a certain critical angle, any flow sufficiently near the corner must consist of a sequence of eddies of decreasing size and rapidly decreasing intensity. The ratios of dimensions and intensities of successive eddies are determined for the full range of angles for which the eddies exist. The limiting case of zero angle corresponds to the flow at some distance from a two-dimensional disturbance in a fluid between parallel boundaries. The general flow near a corner between two plane free surfaces is also determined; eddies do not appear in this case. The asymptotic flow at a large distance from a corner due to an arbitrary disturbance near the corner is mathematically similar to the above, and has comparable properties. When the fluid is electrically conducting, similarity solutions may be obtained when the only applied magnetic field is that due to a line current along the intersection of the two planes; it is shown that the effect of such a current is to widen the range of corner angles for which eddies must appear.

In this paper some approximate results are presented for the problem of the stability of plane Poiseuille flow of a dusty gas, following a formulation given recently by Saffman (1962). It is assumed that the mass concentration of the dust, f, is small, and results are obtained by making a perturbation of the curve of neutral stability for a clean gas, using the approximate solutions given by Stuart (1954). The perturbation equation is expressed in terms of integrals by introducing the adjoint wave function, the calculation of which is described. The integral coefficients were evaluated by numerical integration using a Mercury computer, and the results are illustrated for f = 0.05 by a set of perturbed neutral stability curves at different values of the time relaxation parameter SR varying from 0 to 500. These results, whilst not of great numerical accuracy, are sufficient to show qualitatively how the curve of neutral stability is modified by the presence of the dust.

Consideration is given to the flow of an idealized elastico-viscous liquid contained in the narrow channel between two concentric cylinders, the motion being due to the relative rotation of the cylinders. It is shown that the presence of elasticity in the liquid lowers the value of the critical Taylor number at which instability occurs. The secondary motion arising at the onset of instability has the usual cellular pattern, the cell length being decreased by the presence of elasticity in the liquid.

An investigation is made of the disturbances produced in a closed, gas-filled tube by the oscillations of a piston at one end, when the piston oscillates at near resonant frequencies. Within a well-defined frequency band around each resonant frequency, shock waves appear in the solution; outside this interval the oscillations are continuous, but not purely sinusoidal.

The solution includes the effects of compressive viscosity, and of shear viscosity in the boundary layer at the walls of the tube. For typical laboratory conditions the effect of compressive viscosity is found to be quite small (giving a shock thickness of the order of 10−4in.). The boundary layer effect can be more significant, though the most important modification required of the usual acoustic theory is found to arise from the non-linear terms.

In Part 1 of this paper a free-streamline wake model was introduced to treat the fully and partially developed wake flow or cavity flow past an oblique flat plate. This theory is generalized here to investigate the cavity flow past an obstacle of arbitrary profile at an arbitrary cavitation number. Consideration is first given to the cavity flow past a polygonal obstacle whose wetted sides may be concave towards the flow and may also possess some gentle convex corners. The general case of curved walls is then obtained by a limiting process. The analysis in this general case leads to a set of two functional equations for which several methods of solution are developed and discussed.

As a few typical examples the analysis is carried out in detail for the specific cases of wedges, two-step wedges, flapped hydrofoils, and inclined circular are plates. For these cases the present theory is found to be in good agreement with the experimental results available.

Viscous flow perpendicular to a line (or ‘grating’) of evenly spaced identical cylinders is considered in the case when the spacing between the cylinders is much smaller than their cross-sectional dimensions. Lubrication theory is used to find the pressure drop across the grating and hence the force on each cylinder. A square array (or ‘lattice’) of closely packed cylinders is similarly treated.

The properties of a turbulent flow are often described in terms of velocity correlations in space, in time, and in space-time. In this paper the interpretation of velocity correlation measurements which are made in a region of highintensity turbulence is considered in some detail. Under these conditions it is shown that some account must be taken of the effects of both mean and fluctuating shear stresses which are continuously modifying the turbulent structure. For an almost frozen pattern, for example, in the turbulence behind a grid, the turbulent convection velocity is amost equal to the mean flow velocity, while the space correlation and auto-correlation of the velocity fluctuations are simply related through this velocity. In contrast to this, when the intensity is high, the convection velocity may differ considerably from the mean velocity, while it is shown that different turbulent spectral components appear to travel at different speeds. This means that the turbulent spectrum and the turbulent space scales are no longer simply related. For example, the high-frequency spectral components may be ascribed to both the high-velocity eddies and the small wave-number components acting together.

Experimental results are presented which indicate the conditions under which the assumption of a frozen pattern leads to uncertainties in the subsequent interpretation of the measurements. The measurements also show that the observed difference between the mean and the convection velocity may be qualitatively explained in terms of the skewness of the velocity signals.

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).

A new calculation procedure is developed from the postulate that a unique relation exists between cfFc and RFR where cf is the drag coefficient, R is the Reynolds number, and Fc and FR are functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for both Fc and FR to be deduced empirically, so Fc is calculated by means of mixing-length theory and FR is found semi-empirically. Tables and charts of values of Fc and FR are presented for a wide range of MG and TS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

A general treatment is given of the first-order effects of wall proximity on the increased resistance to translational motions of a rigid particle of arbitrary shape settling in the Stokes régime. The analysis generalizes a previous treatment (Brenner 1962) to the case where the principal axes of resistance of the particle may have any orientation relative to the principal axes of the bounding walls. It is shown that, to the first order in the ratio of particle-to-boundary dimensions, the increased resistance of the particle can be represented by a symmetric, second-rank tensor (dyadic) whose value is independent of particle shape and orientation.