The origin of meandering and braiding of alluvial rivers is re-analysed in terms of stability theory. The flow is described by a two-dimensional model, and the transportation of sediment is separated into bed-load transport and transport of suspended sediment, by use of the improved knowledge of sediment transport mechanisms achieved in recent years. The paper explains why it is important to distinguish between the sediment transported as bed load and that in suspension.

The analysis is able to predict whether a river remains stable or tends to meander or braid.

The results of the stability analysis are compared with laboratory experiments and data from natural rivers, and the agreement is satisfactory.

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.

This paper describes part of a detailed study of the initial region of three annular jets. The configurations are the basic one, without any bullet in the centre, and those with a conical and an elliptical bullet. From the mean velocity and turbulence intensity measurements the initial region can be divided into the initial merging, the intermediate and the fully merged zones. Within these three zones similarity of both the mean velocity and the turbulence intensity profiles has been found. The similarity curves are compared with those for a single jet.

Artificial acceleration and deceleration of the transition process in a two-dimensional wake were attempted. The wake was produced behind a thin aerofoil placed parallel to uniform flow. The sound from a loudspeaker introduced into the wake acted as an artificial disturbance. Various kinds of sound were tested and the effect on the transition was judged by the energy spectrum. Sinusoidal sound of the frequency of the maximum growth rate in the linear region decelerates the transition, whereas sound of a different frequency accelerates it. Sound of two or four frequencies is more effective in accelerating the transition when the frequencies are properly chosen. White noise from the loudspeaker is not effective, but a two-peak noise specially designed for strong nonlinear interaction is the most effective in accelerating the transition process. These results can be explained by two empirical properties of the nonlinear interaction: the growth suppression induced by a large amplitude fluctuation and the stronger interaction between fluctuations of closer amplitudes.

In this paper we assess the importance as a noise source of the well-ordered large-scale structure of a jet. We propose two simple models of the structure: the first emphasizes those features in common with waves that initially grow on an unstable shear layer but eventually saturate and decay, while the second regards the abrupt pairing of eddies as the most significant event in the jet's development. Our models demonstrate the possibility that forcing at one frequency could increase the broad-band noise of a jet, though, for jets with supersonic eddy convection velocities, the sound propagating in the direction of the Mach angle retains the spectrum of the excitation field. These features are consistent with the available experimental data, and strongly support the view that the large-scale structure of jet turbulence provides the dominant contribution to jet noise.

Experimental visualization of natural convective flow was carried out by using several kinds of fluid contained in a narrow vertical rectangular cavity with one vertical wall heated, the opposing vertical wall cooled and the upper and lower walls insulated. The effects of the Prandtl number Pr of the working fluid and the width of the cavity W on the flow pattern are discussed qualitatively in the present paper. The occurrence of flow patterns consisting of unicellular flow, steady secondary flow, tertiary flow and transition (from laminar to turbulent) flow is categorically demonstrated by the photographs taken. Moreover, experimental measurements of the net heat transfer through the vertical fluid layer are given for aspect ratios of 6-30 and Prandtl numbers of 4-12 500.

The two-dimensional wake of a thin flat plate parallel to the stream was maintained laminar and steady at Reynolds numbers up to 3000 in a low-turbulence wind tunnel. Velocity distributions in the wake were measured in detail for Reynolds numbers from 20 to 3000. One of the interesting results is the appearance of a velocity overshoot, namely that the velocity in the outer part of the shear layer exceeds that of the uniform flow in the vicinity of the trailing edge. Comparisons between the experimental results and Goldstein's theoretical predictions show good agreement in the far wake irrespective of the Reynolds number, but not in the near wake even at higher Reynolds numbers, in particular immediately behind the trailing edge.

The results of a companion paper are extended to encompass the flow about smooth, but otherwise general body shapes. The wave behaviour depends on three important parameters, namely the body thickness ratio ε, the quantity δ, which is proportional to the difference between the frozen and equilibrium sound speeds, and the ratio λ of a relaxation time to a characteristic flow time. Both analytical and numerical solutions have been obtained; account is taken of nonlinearity for complete spectra of the three parameters, enabling an assessment to be made of the evolution of the wave forms for a host of situations. In particular, it is possible to predict the structures of the shock waves in various regions, and it transpires that under certain conditions vibrational relaxation can overwhelm other dissipative effects.

The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.

The resonant interactions between topographic planetary waves in a continuously stratified fluid are investigated theoretically. The interacting waves form a resonant triad and travel along a channel with a uniformly sloping bottom. The basic state stratification in the channel is characterized by a constant buoyancy frequency. The existence of solutions to the quadratic resonance conditions is established graphically. Each wave by itself is a bottom-intensified oscillation of the type discovered by Rhines (1970) except for the addition of a small positive frequency correction. This correction must be included to satisfy higher-order terms in the bottom boundary condition. For strong stratification (r2 [Gt ] L2, where r = internal deformation radius and L = channel width), the waves are strongly bottom-trapped and this frequency correction is negligible. For weak stratification (r2 [Lt ] L2) the waves are barotropic and the frequency correction is O(δ), where δ = fractional change in depth across the channel. In many oceanic contexts, δ lies in the range 0·1-0·4 and therefore this correction can produce a significant change in the phase speed. The amplitudes of the waves in the triad obey the classical gyroscopic equations usually encountered in quadratic resonance problems. In particular, the amplitudes evolve on the slow time scale \[ t=O(1/f_0\delta^2), \] which for our scaling assumptions is also O(1/f0Ro), where Ro is the Rossby number.

The results are applied to the Norwegian continental slope region. It is shown that, in this vicinity, there may exist resonant triads consisting of two short, high-frequency waves (periods around 3-4 days) and one long, low-frequency wave (period around 9 days).