The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.

The motion of an electrically conducting, incompressible, viscous fluid in the presence of a magnetic field is analyzed for flow between two parallel disks, one of which rotates at a constant angular velocity. The specific application to liquid metal lubrication in thrust bearings is considered. The two field configurations discussed are: an axial magnetic field with a radial current and a radial magnetic field with an axial current. It is shown that the load capacity of the bearing is dependent on the MHD interactions in the fluid and that the frictional torque on the rotor can be made zero for both field configurations by supplying electrical energy through the electrodes to the fluid.

A theory is proposed in which the stress tensor is a function of the components of the rate of deformation tensor and a symmetric tensor describing the microscopic structure of a fluid. The expression for the stress tensor can be written in closed form using results from the Hamilton-Cayley theorem. This theory is shown to contain Prager's theory of dumbbell suspensions as a special case. By limiting the type of terms in the constitutive equations, various stress components can be evaluated for simple shear. These exhibit non-Newtonian behaviour typical of certain higher polymer solutions.

Some of the results of the anisotropic fluid theory are compared with experimental measurements of normal stress and apparent viscosity. Certain high polymers in solution show good agreement between theory and experiment, at least for low enough values of the rate of shear.

The effects of compressibility, temperature-jump and gaseous adsorption are considered in an attempt to predict the temperature-time history at the interface between a gas and a solid when both the temperature and the pressure of the gas are suddenly changed. It appears that temperature-jump will be the dominant effect, with adsorption contributing significantly in some circumstances. Compressibility is of minor importance during practically-resolvable time intervals. Some experimental evidence which gives tentative support to the results of the analysis is commented upon.

Two simultaneous first-order non-linear equations are derived to give a ’high-flow-rate’ model for the displacement of oil by hot water in a porous medium. The solution of these equations is analysed by the method of characteristics and it is shown that in problems for which thermal capacity dependence on temperature is neglected, the solution will have the properties of a simple wave. The simple wave behaviour gives a rapid method for solving practical systems. When temperature dependence is included in the thermal capacities, it is found that a simultaneous shock in temperature and saturation develops, but the solution will usually approximate quantitatively the simple wave result. Decoupling the equations by using an average saturation in the heat transport equation gives results in reasonable agreement with the coupled case.

The spectrum of atmospheric turbulence is very broad by comparison with spectra in wind tunnels. We introduce the notion of small-scale and large-scale turbulence. Small-scale turbulence consists of a set of disturbances, the scales of which do not exceed the distance to the wall and for which the hypothesis of three-dimensional isotropy is valid in a certain rough approximation. Large-scale turbulence is essentially anisotropic; the horizontal scale in the atmosphere is much larger than the vertical one, the latter being confined to a certain characteristic height H. The horizontal scale varies widely according to the external conditions and characteristics of the medium.

The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c; Oboukhov 1941 a,b) were based physically on Richardson's idea of the existence in the turbulent flow of vortices on all possible scales l < r < L between the ‘external scales’ L and the ‘internal scale’ l and of a certain uniform mechanism of energy transfer from the coarser-scaled vortices to the finer.

In Couette flow between coaxial cylinders, ring-shaped vortices, illustrated schematically in figure 1, develop at a Reynolds number which depends strongly on the geometry of the system, as treated analytically for Newtonian fluids by Chandrasekhar (1958). The problem was first considered by Taylor (1923) who, examining simple (micromolecular) liquids, arrived at an equation for the critical Reynolds number Rei above which instability (vortex formation) would occur when the inner cylinder rotated and the outer is stationary, and when the gap is small compared to the radius.

The problem considered here is concerned with small disturbances of plane Couette flow. As is usual in such problems it is assumed that the disturbance velocities are sufficiently small to allow the Navier-Stokes equations to be linearized. There results a special case of the well-known Orr-Sommerfeld equation and this is solved by an exact method using a digital computer. The problem has previously been considered by several authors, mostly using approximate methods and their results have been compared where possible with those obtained here. It was possible to proceed to values of αR not in excess of 1000 (α being the wave-number of the disturbance and R the Reynolds number of the basic flow), and the results tend to confirm the belief that Couette flow is stable at all Reynolds numbers.

A study is made of the flow into vacuum of a gas initially at rest in a state of uniform pressure and density; the analysis is based on a continuum model. Among the topics discussed are the motion of the gas-vacuum interface, the reflexion of a plane front off a rigid wall, the propagation of compressive waves within such expansions, the escape from a sphere and the collapse of a spherical cavity.

The equations describing the motion of a gas carrying small dust particles are given and the equations satisfied by small disturbances of a steady laminar flow are derived. The effect of the dust is described by two parameters; the concentration of dust and a relaxation time τ which measures the rate at which the velocity of a dust particle adjusts to changes in the gas velocity and depends upon the size of the individual particles. It is shown that if the dust is fine enough for τ to be small compared with a characteristic time scale associated with the flow, then the addition of dust destabilizes a gas flow; whereas if the dust is coarse so that τ is relatively large, then the dust has a stabilizing action.

For plane parallel flow, it is shown that the stability characteristics for a dusty gas are still determined by solutions of the Orr-Sommerfeld equation, but with the basic velocity profile replaced by a modified profile which is in general complex. A simple, although unrealistic, example is used to illustrate some features of the action of dust. It is intended to describe the solution of the modified Orr-Sommerfeld equation for plane Poiseuille flow in a later paper.

The problem of an unstable fluid overturning in a vertical tube filled with porous material is treated by an approximation of boundary-layer type. It is shown that the fluid can experience a pseudo-inertial effect, in which variations in density across the tube exhibit properties analogous to variations of momentum in an inertial flow. The mean fluid density and mean-square vertical velocity over a horizontal cross-section of the tube are related by a pair of hyperbolic equations, for which there exist two systems of characteristics. It is shown that changes in the mean density of the fluid can be propagated as discontinuities. For discontinuities of finite amplitude, two jump conditions are derived, one of which is found to involve an undetermined parameter λ. The theory is applied to the case of a vertical tube containing porous material saturated with water, which is attached at the top to a reservoir filled with an aqueous solution (an analogue of Taylor's (1954) experiment). The motion of a finite discontinuity which arises at the initial unstable interface is calculated by two approximate methods. These results compare satisfactorily with the data from three experiments, using tubes of circular cross-section, provided that the value of λ is about 0·75. If the theoretical interpretation is correct, it appears that convective flow ceases when the vertical density gradient is slightly less than the neutral value.

The gravity-wave response of a semi-infinite liquid to the oscillating pressure Pδ(x) exp (iwt) is given in an asymptotic form that is uniformly valid through the transition zone that separates the dispersion-controlled precursor and the monochromatic steady state. The same problem has been considered previously by Stoker (1957), but his initial conditions were spurious, and he did not seek a uniformly valid asymptotic representation.

The disintegration of a charged liquid jet is examined, and the break-up mechanism inferred from photographic evidence. Gravitational, molecular and electrical forces all contribute to the segmentation of the jet and determine the drop size distribution. The disintegration process is investigated from the point of view of drop generation. The segmentation of the charged jet differs from the known ways in which an uncharged jet is broken into drops.