Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Super-Alfvénic supersonic aligned magnetogasdynamic flow over a cone of finite semi-apex angle, with an attached fast shock wave, is solved numerically. We obtain ‘almond curves’ in the plane of magnetic induction vector variation, analogous to Busemann's ‘apple curves’ for supersonic cone flows, to describe the flow field near the cone. Total surface pressure coefficients, current and vorticity distributions are presented. A closed-form solution of the flow is obtained when a switch-on shock occurs.

The extended Cowley–Imai analogy is derived and employed to obtain explicit equations which allow transcription of gasdynamic perturbation solutions into magnetogasdynamic solutions. The transcription is written down to second order for axisymmetric super-Alfvénic flows of a perfect gas at arbitrary Mach numbers. Speed and field perturbations are shown to vanish in the Alfvénic limit for such solutions, although this is not a property of the exact solution. Van Dyke's supersonic-cone-flow solution is then transcribed and compared with the exact numerical solution over the range 1 < A∞, ≥ 20, 1 < M∞, ≥ 20 for a cone of 5° semi-apex angle, showing excellent agreement which improves with increasing field strength. The large-cone-angle behaviour of the solution is also quite good for the upstream state A∞ = M∞ = 2·0.

A class of laminar rotating free-convective flows over a horizontal boundary in the presence of a strong magnetic field is investigated. The range of applicability of boundary-layer approximations is obtained, as well as a class of similarity solutions valid within a domain of multi-parameter space.

An experimental and theoretical investigation has been carried out to determine the effect of thermal radiation on a natural convection boundary layer formed adjacent to a vertical flat surface with uniform heat flux input. In the experiment, the gases air, argon and ammonia were used as the fluid medium, thus permitting the observation of radiation effects in non-abosrbing and absorbing media. Experimental results were obtained for three different wall emittances at ambient pressures ranging from 2 to 8 atmospheres in air and argon and from 2 to 7 atmospheres in ammonia. An interferometer was used to measure the temperature distributions in the boundary layer and to evaluate the conductive (convective) heat flux from the surface into the fluid medium. The experimental temperature distributions and heat-transfer results obtained in ammonia gas are compared to the predictions of a perturbation analysis developed by the present writers. General agreement between theory and experiment is found. The presence of a radiating gas is seen to increase the convective heat transfer by as much as 40 % for the conditions of the present experiments. The results further indicate that the temperature distributions and wall-temperature gradients are strongly affected by both variations in the surface emittance and variations in gaseous emission and absorption. For non-absorbing gases, the experimental results are found to be in general agreement with existing theory. It is also shown that the experimental temperature distributions agree very well with theoretical predictions obtained by treating the convection and radiation processes as independent and superimposed.

The instability of convection rolls in a fluid layer heated from below is investigated for stress-free boundaries in the limit of small Prandtl number. It is shown that the two-dimensional rolls become unstable to oscillatory three-dimensional disturbances when the amplitude of the convective motion exceeds a finite critical value. The instability corresponds to the generation of vertical vorticity, a mechanism which is likely to operate in the case of a variety of roll-like motions. In all aspects in which the theory can be related to experiments, reasonable agreement with the observations is found.

Existing experiments on the low-speed flow downstream of steps and fences, and some new measurements downstream of a backward-facing step, are used to demonstrate the complicated nature of the flow in the reattachment region and its effect on the slow non-monotonic return of the shear layer to the ordinary boundary-layer state. A key feature of the flow is found to be the splitting of the shear layer at reattachment, where part of the flow is deflected upstream into the recirculating flow region to supply the entrainment; the part of the flow that continues downstream suffers a pronounced decrease in eddy length scale, evidently because the larger eddies are torn in two. This phenomenon will occur in all cases where a shear layer reattaches after a prolonged region of separation, either at low speed or in supersonic flow. For simplicity, the discussion in the present paper is confined to low-speed flows.

The development and evaluation of a hot-film probe, suitable for use within arteries and operated with a commercial constant-temperature anemometer and linearizcr, is described. The performance of the system in the recording of arterial velocity wave forms is described, and instantaneous and time-averaged velocity profiles constructed from measurements in the thoracic aorta of dogs are presented. The profiles were blunt, with boundary layers estimated to be less than 2 mm thick throughout the cycle, and significant skews were observed, the explanation for which appears to lie in the influence of local geometry on the flow. A preliminary study of flow disturbances in the aorta based on visual observation of instantaneous velocity wave forms and frequency spectrum analysis is reported. The occurrence of flow disturbances and turbulence is shown to be related to peak Reynolds number and the frequency parameter α. The possible roles of free-stream disturbances and boundary-layer transition in generating these disturbances are discussed.

Quasi-steady creeping flow in models of small airway units of the lung is investigated. A respiratory unit of the lung is modelled by a sphere, an oblate and a prolate ellipsoid of revolution, and a circular cylinder of finite length. The solution of the Stokes equations for each of these geometries is indicated for general axi-symmetric boundary conditions. For particular cases consistent with the models, streamlines are plotted and some velocity profiles are shown. It is suggested that bulk 00w in the ha1 generations of the lung is significant for gas transport even though diffusion is the predominant mechanism there.

The steady-state interaction between surface waves and long internal waves is investigated theoretically using the radiation stress concepts derived by Longuet-Higgins & Stewart (1964) (or Phillips 1966). It is shown that, over internal wave crests, those surface waves for which cg0cosϕ0 > ci experience a change in direction of propagation towards the line of propagation of the internal waves and their amplitudes are increased. Here cg0 is the surface-wave group speed at U = 0, ϕ0 is the angle between the propagation direction of the surface waves at U = 0 and the propagation direction of the internal waves, and ci is the phase speed of the internal waves. If cg0cos ϕ0 < ci the direction of the surface waves is turned away and their amplitudes are decreased. Over troughs the opposite effects occur.

At positions where the local velocity of surface-wave energy transmission measured relative to the internal wave phase velocity is zero, i.e. cg + U − ci = 0, there is a singularity in the energy of the surface waves with resulting infinite amplitudes. It is shown that at these critical positions two wavenumbers which were real and distinct on one side coalesce and become complex on the other. The critical positions are thus shown to be barriers to the propagation of those wave-numbers. It is also shown that there is a critical position representing the coalescence of three wavenumbers. Surface-wave crest configurations are shown for three numerical examples. The frequency and direction of propagation of surface waves that exhibit critical positions somewhere in an internal wave field are shown as a function of the maximum horizontal surface current. This is compared with measurements of wind waves that have been reported elsewhere.

The propagation of internal Alfvén-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigated in the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolis force is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency Ωd = 0, + ΩA or ± Ω ± (Ω2 + Ω2A)½, where ΩA is the Alfvén frequency and Ω is the Coriolis frequency, and the angular momentum is transferred to the mean flow there by Alfvén-inertio-gravitational waves. Asymptotic solutions to the wave equation are obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layer absorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydro-magnetic flows.