Previous experimental studies are reviewed and those whose data are deemed reliable are identified. New experiments at larger scale are described and the results are reported. These are combined with the reliable previous studies to form a data set covering heights from 3.66 to 50 m and gasflow rates from 0.0002 to 0.59 normal m3/s. These wide-ranging data are combined with an integral theory for bubble plumes to determine functional relationships between local plume properties and the entrainment coefficient and the fraction of the momentum flux that is carried in the turbulent velocity fluctuations. These relationships together with the integral theory provide a set of equations that are suitable for numerical solution for the mean flow properties of any round bubble plume. Examples of the numerical solutions are presented and a comparison of one of these with existing experimental data is given. The relationships between the local plume properties and the entrainment coefficient and the momentum flux carried by the turbulence are interpreted to provide a qualitative understanding of the parameters involved and their influences on the plume.

This paper describes a laboratory experiment designed to compare measurements with published theoretical ideas of the mixed-layer growth of a two-layer system in which the turbulence is induced by an oscillating grid. Experimental results show excellent agreement with an earlier theory by one of us (Long), in which the mixed-layer depth D* measured from a virtual origin is given by $D_{*}\sim V_0^{-\frac{7}{11}}K^{\frac{9}{11}}t^{\frac{2}{11}}$, where K is action, t is time and V0 is a characteristic velocity of the problem. The experiments also verify Long's theoretical entrainment relation E = α2Ri−7/4, where E is the entrainment coefficient and $Ri = D^3_{*}\Delta b/K^2$, and Δb is the buoyancy difference between the two layers. The interfacial-layer thickness was observed to be proportional to the depth of the mixed layer, as also predicted by Long. After a certain depth, the entrainment law tends to deviate from Long's theory. The deviation may be due to wall effects.

The output statistics of a laser anemometer operating in a low particle density are discussed. A rigorous derivation is given for the influence of two popular data-handling algorithms on these statistics. In particular it is shown that the measured statistics can differ from those of the flow statistics and from the particle-arrival statistics. The variables that control the statistical regime are derived and quantitative estimates are given for their ranges of influence.

The first system discussed is a sample-and-hold system where the output is a piecewise-continuous signal obtained by holding the last processor measurement until a new one is obtained. The second system is one where an attempt is made to store all the measurements for processing, but which contains a rate-limiting device. Because of this device, some measurements may be lost when the particle rate is high. This system is referred to as a saturable system.

In both cases it is found that the statistics of the output depend on the product of the mean particle rate and the flow correlation time as well as the flow statistics. The statistics of the saturable system also depend on the ratio of the mean particle rate to the maximum rate at which measurements can be accepted by the system. Because of this, the statistics of both systems depend on the particle density.

Attainable conditions are demonstrated, where the output velocity measurement statistics are essentially identical with the flow statistics.

An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed.

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.

The time-dependent evolution of sheared Rossby waves starting from an initial disturbance is studied for the simple case in which the shear is uniform. The uniform-shear assumption allows explicit solutions to be obtained which are useful in addressing the issue of the long-time asymptotic approach to normal modes and in assessing the relative importance of viscosity, nonlinearity and time-dependence in the evolution of Rossby waves in the presence of critical layers.