The results are presented of an experimental investigation of the flow of mercury along straight, circular and rectangular non-conducting ducts situated in a magnetic field that is uniform except over a short length of the duct where its value decreases by 50%. Magnitudes of the field strength and mean velocity are such that the Hartmann number M is large, the interaction parameter N ≈ M½ and the magnetic Reynolds number Rm [Lt ] 1. In all but one respect this is the prototype problem analysed by Holroyd & Walker (1978): their analysis required that N [Gt ] M½.

Distributions of pressure, electric potential and velocity are measured, the latter by hot-film probes. Qualitative agreement with the theoretical predictions is obtained in so far as a pressure drop of O(duct radius × fully-developed flow pressure gradient × M½) occurs over the non-uniform field region and, in the circular duct, the fluid can be seen to migrate towards the centre of the duct upstream and downstream of the non-uniform field region but in that region this tendency is reversed.

Similar effects appear to occur in the rectangular duct.

Detailed measurements in the wakes behind two-dimensional square section blocks (height h) mounted in thick rough wall boundary layers (height δ) are presented for cases in which h/δ [Lt ] 1. The data provides some insight into the relaxing flow downstream of reattachment, confirming the conclusion of Bradshaw & Wong (1972) that reattaching flows are surprisingly complicated and involve considerable distortion of the separated shear layer. In particular, the measurements show that eddy length scales are considerably reduced and, since the flow eventually relaxes to a boundary layer similar to that upstream, turbulence models based on eddy viscosity concepts cannot, in principle, be expected to be satisfactory. Using the present data this is demonstrated by a more detailed comparison with the theoretical predictions of Counihan, Hunt & Jackson (1974) than has been previously possible. It is shown that, whilst their theory does not predict the behaviour of the turbulent stresses, it does give reasonable agreement with the mean velocity perturbations at least in the near wake −10 < x/h < 30. Except in the near wall region, where the roughness provides the dominant length scale, it is argued that the rate at which the perturbation flow decays is governed largely by the amount by which the separated shear layer is distorted prior to reattachment, which in turn is determined by, say, a turbulence Reynolds number of the body, (hU/v0)h, or, in other words, by the characteristics of the upstream flow at, say, the body height.

The generation of initial wavelets, which appear at the initial stage of the generation and growth processes of wind waves after the abrupt start of the wind on a still water surface, has been investigated by systematic experiments together with theoretical analyses. The energy of the initial wavelets, measured by a resistance-type wave gauge of 50 μm diameter, grew exponentially with time at a constant frequency. The frequency and the growth rate were independent of the fetch but did depend on the friction velocity u*a of the air. The phase velocity of the initial wavelets, measured by a shadowgraph-photography technique, was nearly constant, independent of u*a. A coupled shear flow model in the air and water was examined, to explain the observed characteristics of the initial wavelets in terms of the instability mechanism. The theoretical analysis showed that, for each shear flow pattern observed in the experiments, there exist waves whose growth rate is maximum. The frequency, the growth rate and the phase velocity of these critical waves were virtually coincident with those properties of the observed initial wavelets. It is concluded that the generation of wind waves, whose initial stage is called the initial wavelets, is caused by the selective amplification, by the instability mechanism, of the small perturbations which inevitably occur in the flow.

The limitation of the linear instability theory as applied to the process of further growth of the wind waves is also discussed. From some facts recognized through detailed observations, it is inferred that the phenomena controlled by the linear mechanism last for only about 10 s, and that these evolve to the wind waves which are characterized by inherent nonlinearity.

The motion of a sphere in the presence of a fluid-fluid interface is studied. First, a solution is derived for a point force near a plane interface. Then the solution is extended to include the higher-order terms which are required to describe the motion of a solid sphere. Singularities of higher orders at the centre of the sphere are obtained by using the method of reflexions. For a fluid–fluid interface with an arbitrary viscosity ratio, the drag force and the hydrodynamic torque are calculated for the special cases of motion of a sphere perpendicular and parallel to the interface. In addition, the rotational motion of a sphere is also investigated.

The steady streaming induced by oscillatory viscous flow of small amplitudes over a wavy wall has been analysed, and the computed flow patterns have been found to agree well with the flow patterns visualized experimentally in a tube. When the first parameter, α/δ (the ratio of the wavelength of the wavy wall to the thickness of Stokes layer), becomes larger than about 26, the streaming has a double structure consisting of regions of upper and lower pairs of recirculations. As the second parameter, L/δ (the ratio of the amplitude of the wavy wall to the thickness of Stokes layer), is increased, the upper pair of recirculations squeezes in a gap between the lower recirculations above the troughs of the wall. A similar double structure of steady streamings was also observed above ripple marks formed under oscillatory viscous flow. A bearing is suggested of this phenomenon on the determination of stationary profiles of ripple marks.

This paper uses asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation. When the Nahme–Griffith number is large we show how the flow evolves from Poiseuille flow with a uniform temperature distribution to a plug flow with hot boundary layers on the walls. An asymptotic solution is obtained for the flow in the region of transition from Poiseuille to plug flow and an explicit equation is derived for the pressure gradient in terms of the local downstream co-ordinate in this transition region.

In the early theoretical study of aquatic animal propulsion either the two-dimensional theory or the large aspect-ratio theory has been generally used. Only recently has the unsteady lifting-surface theory with the continuous loading approach been applied to the study of this problem by Chopra & Kambe (1977). Since it is well known that the continuous loading approach is difficult to extend to general configurations, a new quasi-continuous loading method, applicable to general configurations and yet accurate enough for practical applications, is developed in this paper. The method is an extension of the steady version of Lan (1974) and is particularly suitable for predicting the unsteady lead-edge suction during harmonic motion.

The method is applied to the calculation of the propulsive efficiency and thrust for some swept and rectangular planforms by varying the phase angles between the pitching and heaving motions. It is found that with the pitching axis passing through the trailing edge of the root chord and the reduced frequency k equal to 0·75 the rectangular planform is quite sensitive in performance to the phase angles and may produce drag instead of thrust. These characteristics are not shared by the swept planforms simulating the lunate tails. In addition, when the pitching leads the heaving motion by 90°, the phase angle for nearly maximum efficiency, the planform inclination caused by pitching contributes to the propulsive thrust over a large portion of the swept planform, while, for the rectangular planform, only drag is produced from the planform normal force at k = 0·75. It is also found that the maximum thrust is not produced with maximum efficiency for all planforms considered. The theory is then applied to the study of dragonfly aerodynamics. It is shown that the aerodynamically interacting tandem wings of the dragonfly can produce high thrust with high efficiency if the pitching is in advance of the flapping and the hindwing leads the forewing with some optimum phase angle. The responsible mechanism allows the hindwing to extract wake energy from the forewing.

A study is made of the flow and the shape of the free surface of a non-Newtonian fluid contained in a flat-bottomed cylindrical vessel performing torsional oscillations of small amplitude. For the case where the fluid depth is small compared with the vessel radius, the solution is shown to have a simple radial dependence except in a boundary-layer region near the side wall. It is shown that under certain circumstances the mean steady second-order components of both free surface curvature and radial–axial flow may be in the reverse direction to those for a Newtonian fluid. It is found that flow reversal may occur at any frequency of oscillation, but that surface curvature reversal cannot occur at low frequencies.

Hoverming motions, by which an animal (or a helicopter) in stationary fluid generates a downflow to support its weight, entail energy costs that include the induced power (power supplied to that downflow). The simplest classical model for induced power is the actuator-disk model. This paper shows how a relatively insignificant modification can be made to that model to make it aerodynamically self-consistent. The modified simple model of the downflow may be evaluated in fluid that either is unbounded or is bounded below by horizontal ground. Comparison of the calculated induced powers in the two cases (even though made in this paper not for the true axisymmetric flow patterns but for the corresponding two-dimensional flow patterns) appears to give a more satisfactory analysis than was previously available of the observed reduction of induced power associated with proximity to the ground.