It is suggested that giant waves, as observed on the Agulhas Current, occur where the wave groups are reflected by the current. The local behaviour of the wave amplitude is modelled by the nonlinear Schrodinger equation

iar = aρρ-ρ+β|a|2a.

For waves of a given incident wave amplitude the steady solutions are stable.

Reflexion coefficients greater than unity have now been predicted for a variety of different systems involving waves propagating towards a shear layer, but almost invariably only in regions of parameter space for which the layer exhibits Kelvin-Helmholtz instability. This paper contains a study of two examples in which, for appropriate parameter values, there are no such instabilities to obscure (or even prevent) the ‘over-reflexion’ of an incident wave, namely (a) hydro-magnetic internal gravity waves meeting a vortex-current sheet in a stratified fluid and (b) magneto-acoustic waves meeting a vortex sheet in a compressible fluid. In the former case the energetic aspects of over-reflexion are examined in detail, thus displaying the way in which the excess reflected energy is extracted from the mean motion and the sense in which the transmitted wave may be viewed, by analogy with certain concepts employed in plasma physics, as a carrier of so-called ‘negative energy’.

This paper describes an investigation into the response of both the pulsed-wire anemometer and the hot-wire anemometer in a highly turbulent flow. The first part of the paper is concerned with a theoretical study of some aspects of the response of these instruments in a highly turbulent flow. It is shown that, under normal operating conditions, the pulsed-wire anemometer should give mean velocity and longitudinal turbulent intensity estimates to an accuracy of better than 10% without any restriction on turbulence level. However, to attain this accuracy in measurements of turbulent intensities normal to the mean flow direction, there is a lower limit on the turbulent intensity of about 50%. An analysis is then carried out of the behaviour of the hot-wire anemometer in a highly turbulent flow. It is found that the large errors that are known to develop are very sensitive to the precise structure of the turbulence, so that even qualitative use of hot-wire data in such flows is not feasible. Some brief comments on the possibility of improving the accuracy of the hot-wire anemometer are then given.

The second half of the paper describes some comparative measurements in the highly turbulent flow immediately downstream of a normal flat plate. It is shown that, although it is not possible to interpret the hot-wire results on their own, it is possible to calculate the hot-wire response with a surprising degree of accuracy using the results from the pulsed-wire anemometer. This provides a rather indirect but none the less welcome check on the accuracy of the pulsed-wire results, which, in this very highly turbulent flow, have a certain interest in their own right.

The pulsed-wire anemometer has enabled velocity measurements to be made in a variety of unsteady turbulent flows. So far the use of the instrument has been confined to the determination of mean velocity, turbulence intensity and probability density. Here we show how spectral information can also be obtained. The instrument provides estimates of the velocity by measuring the time of flight of a heated flow tracer. Periodic samples of velocity can be generated by driving the anemometer with a regular train of pulses, but unfortunately it is not possible to pulse the heater at a rate greater than about 50 or so times per second, without risk of burning out the wire. This limits the spectral information that can be obtained to situations where all the energy occurs at frequencies below 25 Hz. The random sampling scheme used here avoids the aliasing problem inherent in periodic sampling and enables estimates of power spectral density to be formed up to frequencies many times the average sampling rate. This technique is used to obtain spectral estimates of the velocity fluctuations that arise at various locations in the wake of a flat plate.

The stability of three axisymmetric jet profiles is reviewed. These profiles represent the development of an incompressible jet from a nearly top-hat profile to a fully developed jet profile. The disturbance equations for arbitrary mode number in a region of zero shear, which provide the boundary conditions for the numerical solution, are solved analytically through use of the disturbance vorticity equations. Numerical solutions for the spatial stability for the axisymmetric (n = 0) disturbance and the asymmetric n = l disturbance are presented. Previously published calculations of least stable modes are shown to be incorrectly interpreted and their actual mode types are given. The critical Reynolds number is found to increase as the profile varies from a top-hat to a fully developed jet form. Closed contours of constant amplification, which are unusual in free shear flows, are shown to exist for the n = 1 disturbance in the fully developed jet region. A fluctuation energy balance is used to justify the occurrence of this destabilizing effect of decreasing Reynolds number.

The bursting process in turbulent boundary layers provides new insight on turbulence phenomena, mechanics of sedimentation, and genesis of bedforms in natural geophysical flows. Recent visualization experiments suggest that the turbulent boundary layer can be divided into an inner zone, whose essential characteristics scale with inner (wall) variables, and an outer zone, whose properties scale with the fluid-dynamic variables of the entire flow. The inner zone is distinguished by (i) a viscous sublayer displaying spanwise alternations of high-and low-speed streaks and (ii) episodic disruption by lift-ups of low-speed streaks. Oscillatory growth and breakup stages of the Stanford model of bursting characterize the turbulent structure of the outer zone. The burst cycle exists in turbulent boundary layers of all natural flows except perhaps (i) open-channel flows in the upper part of the upper flow regime and (ii) wind-generated surface waves.

Fluid motions described as kolks and boils in incompressible open-channel flows correspond to the oscillatory growth stage and the late oscillatory growth and breakup stages, respectively, of the Stanford model of bursting. Supporting evidence includes (i) close similarity of gross fluid motions, (ii) equivalent scaling of boils and bursts, and (iii) intensification of boils and bursts in adverse pressure gradients and over rough beds. McQuivey's (1973) turbulence measurements show that the Eulerian integral time scale TE scales with the same outer variables as boil periodicity and burst periodicity. It is hypothesized that TE equals the mean duration of bursts at a point in the flow.

Bedforms governed by the turbulent structure of the inner zone (microforms) cannot form if the sublayer is disrupted by bed roughness. The conditions for the existence of two common microforms and their spacings scale with the inner variables. Grain roughness increases the vertical intensity of the turbulence (by enhancing lift-ups) within the inner zone, thereby explaining textural differences between the coarse ripple and fine ripple bed stages of Moss (1972).

Mesoforms respond to the fluid-dynamical regime in the outer zone and scale with the outer variables. The mean spacing of dunelike large-scale ripples in equilibrium open-channel flows is proportional to the boundary-layer thickness and equals the length scale formed by the product of the free-stream velocity and the boil period.

Strong upward flow in a burst provides the vertical anisotropy in the turbulence which is needed to suspend sediment. Bursting promotes the entrain-ment of more and coarser sediment than tractive forces alone can accomplish.

A higher-order lifting-line theory for a wing in unsteady motion is discussed. Apart from the addition of higher-order terms, it also differs from the theory derived by James (1975) in its emphasis on ‘physical’ interpretations. This emphasis has made it possible to shed some new light on Prandtl's classical lifting-line theory, as well as on Weissinger's 3/4-chord theory.

The selective withdrawal of a layered fluid from a reservoir has interesting properties which are not present if the stratification is continuous. The problem investigated is that of finding the ratios of the discharges from each flowing layer when the total discharge from all layers is regulated at the outlet. It is shown that the ratios are determined by the requirement that the flow be smooth at critical points in the flow, each critical point being a point at which the long-wave velocity on one of the interfaces is zero. If there are too many critical points, the flow is over-determined and becomes unsteady. It follows therefore that if the external conditions change slowly, such as in the slow draining of a reservoir, the flow alternates between intervals in which the flow ratios also change slowly and intervals in which the flow ratios oscillate unsteadily. An experiment is described in which the theoretical conclusions were tested for two-layer flow. Good agreement was obtained between theory and experiment.

In Poiseuille flow in a circular tube passive contaminant initially spread uniformly over the cross-section would be pulled out in a paraboloidal snout in the absence of any diffusive mechanism, and there would be a discontinuity in $\overline{C}$, the mean concentration over the cross-section, associated with the contaminant at the front of the snout. In reality molecular diffusion smooths out this snout in two ways: direct longitudinal diffusion and the interaction between lateral diffusion and advection. The effect of these two mechanisms is discussed, and determined for small values of κt/a2, where t is the time since injection, κ is the molecular diffusivity and a is the tube radius. For such values, important in many applications, the tube walls play no part in the smoothing process. It is shown that for $\kappa t/a^2 < 0.25(\overline{u}a/\kappa)^{-\frac{2}{3}}$, where $\overline{u}$ is the discharge velocity, the effect of longitudinal diffusion dominates over that of the interaction, which is, in turn, dominant for $\kappa t/a^2 > 2.5(\overline{u}a/\kappa)^{-\frac{2}{3}}$, when $\overline{C}$ is close to the form described by Lighthill (1966).

What transient motions occur as a fluid responds to gravitational forces in a rotating channel, and what equilibrium does the fluid adjust to? This problem is studied to illustrate how boundaries affect the process of adjustment to a geostrophic equilibrium. In particular, linear solutions are found for an infinitely long channel of constant width and constant depth when there is an initial discontinuity in the level of the free surface. The results are summarized in the figures, and can be described in terms of Poinearé waves and Kelvin waves. When the channel is wide compared with the Rossby radius, the final state involves a current of that width which follows the left-hand boundary (for Northern-Hemisphere rotation) to the position of the initial discontinuity, then crosses the channel and continues downstream along the right-hand wall.