The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.

In order to elucidate the importance of the infinite conductivity assumption in MHD a simple problem has been studied. This is a Rayleigh-Taylor problem of two superposed fluids under gravity partially stabilized by a uniform, horizontal magnetic field. It is found that the inclusion of a small, but finite resistivity introduces new and unexpected solutions. For instance, moderately long, stabilized’ waves are now found to grow aperiodically and unexpectedly rapidly at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$). Other modes are found to be periodic and damped at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$).

The problem described by the title is investigated when the magnetic field is uniform and parallel to the velocity on the two sides of a surface of discontinuity of velocity in an electrically conducting inviscid fluid. The secular equation depends on two parameters β and N, where β is the ratio of magnetic Reynolds number to dimensionless wave number and N is the ratio of the magnetic to the kinetic energy of the fluid. It is found that the flow is unstable for all values of β and N.

This note describes the slow magneto-hydrodynamic flow of hydrochloric acid in a helix. At very low Reynolds number a transverse magnetic field is found to retard the flow in agreement with existing theory and with existing experimental results obtained using mercury. At higher Reynolds numbers where secondary flow in a helix becomes important the transverse magnetic field is found to reduce this secondary flow.

Small disturbances relative to a horizontally stratified shear flow are considered on the assumptions that the velocity and density gradients in the undisturbed flow are non-negative and possess analytic continuations into a complex velocity plane. It is shown that the existence of a singular neutral mode (for which the wave speed is equal to the mean speed at some point in the flow) implies the existence of a contiguous, unstable mode in a wave-number (α), Richardson-number (J) plane. Explicit results are obtained for the rate of growth of nearly neutral disturbances relative to Hølmboe's shear flow, in which the velocity and the logarithm of the density are proportional to tanh (y/h). The neutral curve for this configuration, J = J0(α), is shown to be single-valued. Finally, it is shown that a relatively simple generalization of Hølmboe's density profile leads to a configuration having multiple-valued neutral curves, such that increasing J may be destabilizing for some range (s) of α.

Consideration is given to the flow of an idealized elastico-viscous liquid in a curved pipe under a pressure gradient. By using the series expansion method of Dean (1927, 1928) in powers of a/R where a is the radius of the pipe and R the radius of curvature of its ‘central line’, it is shown that the general nature of the motion is similar to that of the motion of a Newtonian viscous liquid, the liquid elements moving along the pipe in two sets of spirals separated by the central plane. However elasticity of the type considered could strongly affect the pitch of these spirals. To the approximation considered, the flow pattern of the elastico-viscous liquid depends only on the limiting (zero-shear-rate) viscosity η0 and the first moment, K0, of the distribution of relaxation times. The corresponding stress components involve also the second moment of this distribution.

It is also shown that the presence of elasticity in the liquid increases the rate of discharge of the liquid.

The propagation of a one-dimensional combustion wave into a non-ionized gas at rest in the presence of an electromagnetic field is considered when ionization of the gas occurs across either the combustion wave or a preceding shock wave. The electric and magnetic fields in the undisturbed gas ahead of the waves are mutually perpendicular and orthogonal to the direction of wave propagation. It is shown that steady detonation occurs at a point which is analogous to the Chapman-Jouguet point of ordinary gasdynamic combustion theory. Numerical calculations are made of the state of the gas between and behind the waves in two particlar models, in both of which the upstream electric field is zero. The models are then equivalent to magnetogasdynamic phenomena in a perfectly conducting gas. First, the case of steady detonation is studied. Secondly, steady deflagration in a tube, closed at one end, is discussed.

Asymptotic forms, valid for high Hartmann number M, are obtained for the mean velocity for laminar magnetohydrodynamic flow in a rectangular tube. For a tube with non-conducting walls it is found that, neglecting exponentially damped terms, the mean velocity can be expressed in closed form in terms of tabulated functions. The first three terms of the expansion of the mean velocity in inverse powers of M are in extremely close agreement with a corresponding expansion obtained by Shercliff (1953) using a boundary-layer method.

For perfectly conducting walls the first five terms of an expansion in inverse powers of M are obtained.

Quartz fibre anemometers have been used (as described in subsequent papers) to survey the velocity field of turbulent free convective air flows. This paper discusses the reasons for the choice of this instrument and provides the background information for its use in this way. Some practical points concerning fibre anemometers are mentioned. The rest of the paper is a theoretical study of the response of a fibre to a turbulent flow. An approximate representation of the force on the fibre due to the velocity field and the equation for a bending beam, representing the response to this force, form the basis of a consideration of the mean and fluctuating displacement of the fibre. Emphasis is placed on the behaviour when the spectrum of the turbulence is largely in frequencies low enough for the fibre to respond effectively instantaneously (as this corresponds to the practical situation). Incomplete correlation of the turbulence along the length of the fibre is taken into account. Brief mention is made to the theory of the higher-frequency (resonant) response in the context of an experimental check on the applicability of the low-frequency theory.

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion.

Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments.

The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.