Precise theoretical relations between statistical characteristics of turbulent velocity and an electrical field are found for homogeneous and isotropic turbulence in the presence of a uniform magnetic field. These include turbulence intensities, correlations and spectra and relations allowing estimation of the degree of anisotropy of a turbulent flow. The theoretical results are verified by experiments with flow of very dilute salted water past a grid in the presence of a uniform magnetic field. The theoretical and the experimental results are in good agreement. Preliminary results of vorticity measurements are also presented.

The equation for small-amplitude disturbances to an unbounded flow of constant shear on a beta-plane has well-known solutions of a particularly simple form. In physical terms such solutions represent a flow in which absolute-vorticity contours, initially taking a wavy configuration, are deformed by the basic-state shear. Here it is shown that, at least in cases where the initial disturbance has long wavelength, the vorticity distribution predicted by such solutions eventually becomes barotropically unstable, as the shearing over of material contours leads to local reversals in the cross-stream gradient of absolute vorticity.

Low-Reynolds-number, mildly curved, turbulent channel flow has been simulated by direct numerical solution of the Navier – Stokes equations. Computed velocity fields were found to be in good agreement with experimental measurements. The resulting flow fields were used to study the effects of streamline curvature by comparing the concave and convex sides of the channel. Observed effects are consistent with experimental measurements for mild curvature. The most significant difference in the turbulence statistics is in the Reynolds shear stress. This is accompanied by significant differences in the terms of the equation for Reynolds-shear-stress budget. In addition, it was found that stationary Taylor – Görtler vortices were present and that they had a significant effect on the flow by contributing to the mean Reynolds shear stress, enhancing the asymmetry of the channel, and affecting the underlying turbulence.

A theoretical study has been made of the laminar boundary layer on a semi-infinite flat plate parallel to a stream consisting of a uniform steady component U∞ normal to its leading edge and a periodic sideslip component of the travelling-wave type, where the wave travels with velocity Q in the direction of the steady component. It is found that the longitudinal flow (that in planes perpendicular to the leading edge) is independent of the transverse flow, and satisfies the well-known Blasius equations. The transverse flow is governed by a linear partial differential equation which may be approximated in different ways for high and low values of the ‘reduced’ frequency $\overline{\omega}$. A series-expansion solution for small $\overline{\omega}$ appears to be valid up to about $\overline{\omega} = 2$; the solution for large $\overline{\omega}$ is applicable down to $\overline{\omega} \approx 10$. A third approximation has been developed which joins the others smoothly. Numerical solutions of the equations for the transverse flow are presented for $0 \leqslant\overline{\omega}\leqslant 40$ and Q/U∞ = 0.6 (the value appropriate to the Queen Mary College (QMC) ‘gust-tunnels’) and for $\overline{\omega} = 10$ and 0.4 [les ] Q/U∞ [les ] ∞. The value of Q/U∞ has a profound influence: for values less than about one there are large phase lags within the boundary layer; for large values there are phase leads throughout most of the layer. For Q/U∞ < 1 the amplitude of the oscillation within the boundary layer exceeds that of the external driving oscillation, this ‘overshoot’ increasing as the wave-speed ratio diminishes. At Q/U∞ = 0.6 peak velocities more than 3 times those outside appear within the viscous layer.

As $\overline{\omega} \rightarrow \infty $, the transverse viscous layer becomes thinner; the oscillatory boundary layer, here transverse, becomes a ‘Stokes layer’ and is virtually uncoupled from the longitudinal flow. Far downstream the amplitude of the transverse skin-friction grows as x½ and becomes comparable with the streamwise component even for moderate values of the sideslip amplitude.

Experiments were conducted in one of the QMC gust-tunnels for values of $\overline{\omega}$ up to 2.0. Measurements of the transverse velocity amplitude and phase profiles confirm the ‘low frequency theory’.

Liquid flow in a baffled stirred reactor vessel driven by a six-blade disk impeller has been investigated experimentally. Laser-slit photography provided an overview of the flows which were quantified by measurements of velocity characteristics, obtained with a laser-Doppler anemometer, for an impeller rotational speed of 300 r.p.m. and for three impeller clearances from the bottom of the vessel. The mean flow results show an inclination of the impeller stream and the formation of ring vortices above and below the impeller, which depend on the clearance; the flow was strongly three-dimensional with large regions having circumferential velocities in a direction opposite to that of the impeller rotation. Impeller-induced torque measurements show that the Power number is invariant with clearance for turbulent-flow Reynolds numbers ([ges ] 40000) and increases with impeller diameter. The flow structure was controlled mainly by convection and pressure forces with turbulent mixing important in the impeller region.

As a viscous fluid in a vertical tube drains under the effect of gravity, a finger of air rises in the tube. The shape of the interface and the rate at which the finger rises is determined numerically for different values of the dimensionless parameter G = ρgb2/T, where ρ is the density difference between the viscous fluid and the air, b is the radius of the tube, and T is the interfacial tension. A relationship between the Bond number G and the capillary number Ca = μU/T is found and compared with the perturbation result of Bretherton (1961), where μ is the viscosity of the fluid and U is the constant velocity at which the finger rises. The numerical results support Bretherton's conclusions for very small values of Ca and extend the relationship between G and Ca to a region where the perturbation expansion is no longer valid. The results are also valid for long bubbles rising in a tube.