The stability of cellular convection flow in a layer heated from below is discussed for Rayleigh number R close to the critical value Rc. It is shown that in this region the stable stationary solution is determined by a minimum of the integral \[ \int_0^{H_0}R(H)\,dH, \] where R(H) is a functional of arbitrary convective velocity fields which satisfy the boundary conditions. For the stationary solutions R(H) is equal to the Rayleigh number. H0 is a given value of the convective heat transport. In a second part of the paper explicit results are derived for the convection problem with deviations from the Boussinesq approximation owing to the temperature dependence of the material properties.

The interval of Rayleigh numbers in Bénard convection corresponding to cellular motion is determined in the case of free-free boundaries, rigid-free boundaries and rigid-rigid boundaries, taking into account the variation of the kinematic viscosity with temperature. Neglecting the effect of surface tension, it is shown that this interval is largest for the rigid-rigid case. The most important feature from the obtained formula (6.1) is, however, that the interval is extremely dependent on the depth of the fluid layer. To obtain a cellular pattern it is therefore necessary to have very small fluid depths. For example, with Silicone oil and a fluid depth of 7 mm, cellular motion will, according to the theory, be observed for Rayleigh numbers larger than the critical value and less than 1·07 times the critical value. For a fluid depth of 5 mm, however, the formula (6.1) gives that cellular motion will be observed for Rayleigh numbers up to 1·54 times the critical value.

These studies constitute an extension of the work of Doyle, Moffett & Vonnegut (1964).

Experiments showed that the evaporation of a charged droplet of water, aniline or toluene supported in a vertical electric field is accompanied by no discernible loss of charge and a consequent increase in electrical pressure in the drop surface owing to the decrease in radius. When the relationship between drop charge Q and radius R becomes consistent with the Rayleigh criterion the drop disintegrates at its uppermost point, where the electrical pressure is a maximum, to eject about 25% of its mass in the form of highly charged droplets. The measured relationship between the quantity of ejected charge, ΔQ, the mass loss, ΔM, and R was close to that derived theoretically from Rayleigh's equation, indicating that the value of ΔQ for a particular ΔM and R is approximately the theoretical minimum and that an individual drop may undergo a sequence of disintegrations, as was observed. The range of droplet radii studied by means of this technique was 30–200 μ.

The absence of disintegrations during the evaporation of much larger charged drops suspended from insulating fibres was attributed to corona discharge.

A normal magnetic field has a destabilizing influence on a flat interface between a magnetizable and a non-magnetic fluid. Stabilizing influences are provided by interfacial tension and gravity if the lighter fluid is uppermost. The critical level of magnetization for onset of the instability is derived for a fluid having a non-linear relation between magnetization and magnetic induction. Experiments using a magnetizable fluid, which contains a colloidal suspension of ferromagnetic particles, at interfaces with air and water are made and cover a wide range of density differences. Measurements confirm the prediction for critical magnetization, and it was found that, after onset, the interface took a new form in which the elevation had a regular hexagonal pattern. The pattern was highly stable, and the measured spacing of peaks agreed reasonably with that derived from the critical wave-number for the instability of a flat interface.

The acoustic streaming of an idealized elastico-viscous fluid near a cylindrical obstacle is considered using the boundary-layer type of approximation. It is shown that this streaming phenomena can be greatly influenced by the presence of elasticity in the fluid.

The paper discusses the reflexion of a shock wave off a rigid wall in the presence of a boundary layer. The basic idea is to treat the problem not as a reflexion but as a refraction process. The structure of the wave system is deduced by a simple mapping procedure. It is found that a Mach stem is always present and that the bottom of this wave is bifurcated—called a lambda foot. The reflexion is said to be regular if the Mach stem and the lambda foot are confined to the boundary layer and irregular if either extends into the main stream. Two types of regular reflexion are found, one that has reflected compression waves and the other that has both reflected compression and expansion waves. Initial conditions are given that enable one to decide which type will appear. There are also two types of irregular reflexion, one that has a Mach stem present in the main stream and the other that is characterized by a four-wave confluence. Finally there are also two processes by which regular reflexions become irregular. One is due to the formation of a downstream shock wave that subsequently sweeps upstream to establish the irregular system and the other is due to boundary-layer separation which forces the lambda foot into the main stream.

The stability of a periodic internal wave has been investigated experimentally and theoretically. From the analysis it is found that if a primary wave, with wave-number k0 and frequency ω0, is perturbed by two infinitesimal wave-like disturbances with wave-numbers k1 and k1 + k0 and frequencies ω1 and ω1 + ω0, exponential growth of these disturbances will take place under certain conditions. The analysis also indicates which resonantly interacting disturbances can induce an instability and, when viscous dissipation is accounted for, predicts the minimum amplitude for which a wave is unstable. Experimental results demonstrate that this type of instability can cause the breakdown of a first mode internal wave propagating in a fluid composed of two layers of uniform density separated by a thin region in which the density varies continuously.

Nonlinear resonant wave triads composed of one finite and two infinitesimal components are unstable for sum interactions and neutrally stable for difference interactions. A similar criterion holds for tertiary interactions.

Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls.

Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented.

Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.

The differential equation for the vertical velocity of a gravity wave in an inviscid shear flow is singular at a level where the mean fluid velocity is equal to the horizontal phase velocity of the waves. It has been shown that a wave travelling through such a layer has its amplitude attenuated by a constant factor dependent on the local Richardson number. In this paper the results obtained by solving numerically the full sixth order differential equation, which is derived by including viscosity and heat conduction in the problem, (and is not singular) are discussed, and the same attenuation factor is found. Some experiments which confirm certain aspects of the theory are described in an appendix.

A strong sound field in a liquid may generate small cavities that move rapidly through the liquid. This paper is an analysis of the equilibrium states, and the conditions for their stability, of a cavity in translational motion through an inviscid, incompressible liquid. A principal conclusion is that translating cavities have a stable size and shape for a wide range of conditions. The equilibrium shape of a stable cavity is approximately an oblate spheroid. It is also found that the presence of translational motion contributes an outward dynamic pressure that tends to enlarge the cavity. As a result, the equilibrium radius of a translating cavity is greater than the equilibrium radius of the same cavity at rest.

Two interesting linear relations between normal vorticity and current density generated behind a shock wave in three-dimensional unsteady flows of conducting gases have been investigated in order to determine them purely from dynamical considerations. Some interesting physical conclusions have also been made.

This paper indicates the existence of a dual solution of the boundary-layer equations for the flow near a nodal point of attachment of the external flow; especial note is made of the non-axisymmetric boundary-layer flow when the external flow is axisymmetric.

The drag of spheres and disks has been measured in a flow of liquid sodium within an aligned magnetic field. A slightly viscous, strong field limit is discussed and explored experimentally. In this limit the drag coefficient was found to have an asymptotic dependence proportional to the square root of the interaction parameter, the ratio of magnetic to inertial force, independent of body shape. A physical model is presented along with preliminary verification of its basic characteristics.