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.

A theory is given for predicting the absorption of the power in an incident sinusoidal wave train by means of a damped, oscillating, partly or completely submerged body. General expressions for the efficiency of wave absorption when the body oscillates in one or, in some cases, two modes are given. It is shown that 100% efficiency is possible in some cases. Curves describing the variation of efficiency and amplitude of the body with wavenumber for various bodies are presented.

A new laser device has been used to make direct wave-slope measurements in the capillary-gravity range. Owing to the design principles, the digital nature of the system and the use of a laser beam as a probe, the earlier problems of intensity variations and meniscus effects were avoided. Using this new technique, wave-slope spectra both down and across the channel were obtained for different wind conditions, along with corresponding mean-square slope values. Comparisons are made with existing data. The results indicate that a quasi-equilibrium state may exist for each wind speed and that it increases in intensity with increasing wind, which may imply an asymptotic nature for the equilibrium-range coefficient Caa. From the data, two significant frictional velocities, 17.5 and 31 cm/s respectively, are identified as critical values for different ranges of wave development.

In this paper, it is shown that if two spheres of equal radii are placed axisymmetrically in a steady Stokes stream, separation of the flow from the spheres occurs if the distance between their centres is less than approximately 3-67 times the sphere radius. For spheres whose spacing is less than this value, wakes form on both spheres and the fluid within the wakes moves in closed eddy type motion. When the distance between the centres of the spheres is less than approximately 3.22 times the sphere radius, a cylinder of fluid links both spheres, and within this cylinder the fluid rotates in one or more ring vortices, the number of vortices increasing as the distance between the spheres is decreased. When the spheres are in contact, the fluid rotates in an infinite set of nested ring vortices.

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’.

We generalize Crapper's exact solution for capillary waves on fluid of infinite depth. We find two finite-depth solutions involving elliptic functions. We show they can also be interpreted as large amplitude symmetrical and antisymmetrical waves on a fluid sheet. Particularly interesting are the waves obtained from our solution in the limit when the fluid sheet is extremely thin.

A calculation is given of the velocity which a cloud of identical gas bubbles acquires when the liquid in which the cloud is immersed is impulsively accelerated. From the results an expression follows for the effective virtual mass of a bubble in a gas-bubble/liquid mixture. Further consideration is given to that part of the momentum flux in the mixture associated with relative motion between liquid and bubbles. An expression for this quantity is derived which appears to differ from the one used in practice. It is shown that qualitative support for the expression obtained here is provided by experimental observations reported in the literature.

A semi-theoretical study has been made of the problem of stable turbulent heat and mass transfer between a water surface and surrounding atmosphere under the influence of wind. The equations derived are based on the principle of similarity and are therefore expected to be valid under both laboratory and field conditions. The predicted heat- and mass-transfer Stanton numbers appear to be in satisfactory agreement with the available field data.

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 problem of the flow generated in a viscous fluid by the impulsive motion of a wavy wall is treated as a perturbation about the known solution for a straight wall. It is shown that, while a unified treatment for high and low Reynolds numbers is possible in principle, the two limiting cases have to be treated separately in order to get results in closed form. It is also shown that a straightforward perturbation expansion in Reynolds number is not possible because the known solution is of exponential order in that parameter. At low Reynolds numbers the waviness of the wall quickly ceases to be of importance as the liquid is dragged along by the wall. At high Reynolds numbers on the other hand, the effects of viscosity are shown to be confined to a narrow layer close to the wall and the known potential sohtion emerges in time. The latter solution is a good illustration of the interaction between a viscous fluid field and its related inviscid field.

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.

A bispectral analysis of high Reynolds number turbulent velocity-derivative data is carried out. The computations suggest that contributions of wavenumber triplets to the rate of vorticity production and spectral transfer are non-local in wavenumber space and comparable over the whole range of wavenumbers studied. Statistical resolvability of the bispectral estimates is obtained. An appendix on the asymptotic behaviour of bispectral estimates is given.

The stability of liquid films adjacent to supersonic streams was investigated experimentally and compared with analytical results. Linear theories predict that films adjacent ta supersonic streams are much more unstable than those adjacent to subsonic streams. However, our supersonic experimental observa-tions indicated that the liquid film was stable with no entrainment under all test conditions. These conditions included laminar and turbulent boundary layers, a variation in the liquid Reynolds number (based on flow rate) from 1 to 200 and a variation in the free-stream unit Reynolds number from 1.6 × 106 m−1 to 110.0 × 106 m−1. These experimental observations can be explained by nonlinear theories, which predict that linear unstable disturbances do not grow indefhitely but achieve steady-state amplitudes in the supersonic case. The different aspects of the observed wave behaviour such as frequency, wavelength and amplitude are discussed and compared with previous experimental observations and the nonlinear theories.

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.

Experiments were carried out in the turbulent boundary layer on a slightly heated plate in order to establish, mainly for the larger scales of motion, any analogy that may exist between the temperature and velocity fluctuations. With this goal in mind, the spectra and cospectra of the temperature and velocity fluctuations were measured. In particular, the cospectra were obtained by the ‘fluctuation-diagram method’. It soon became evident that the temperature spectrum, except very close to the wall, differs strongly from the spectrum of the longitudinal velocity component. At least for the lower frequency spectral range, which includes about 80% of the total variance, the experimental results support an analogy between the temperature spectrum and a new type of spectrum consisting of the sum of the spectra of the three velocity components weighted by their relative energy. This analogy was established throughout most of the boundary layer.

The Wedemeyer model describing the spin-up of a fluid in a rotating cylinder is generalized to include the case of spin-down. Attention is focused on spin-up and spin-down at a finite (constant) acceleration for small Ekman numbers En. It is found that when the full nonlinear Ekman suction is included for spin-up from rest, the characteristics near the propagating wave front intersect, thus yielding an O(1) velocity discontinuity for the inviscid model. This anomalous behaviour is limited to only a small range of Rossby numbers and does not appear in any of the spin-down solutions. Transient spin-down velocity profiles in the O(E1/4Ω) shear layer at the cylindrical wall are calculated for the quasi-steady flow which occurs for sufficiently small decelerations. Results for impulsive spin-up and spin-down between infinite parallel plates are presented and compared with the asymptotic solutions given by Greenspan & Weinbaum and Benton. Finally, characteristic spin-up and spin-down times are computed for both the contained cylinder and the infinite-parallel-plates geometry.

Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

Using the Orr-Sommerfeld equation with the wavenumber as the eigenvalue, a search for higher eigenstates in the stability theory of the Blasius boundary layer has revealed the existence of a number of viscous states in addition to the long established fundamental state. The viscous states are discrete, belong to two series, and are all heavily damped in space. Within the limits of the investigation the number of viscous states existing in the layer increases as the Reynolds number and the angular frequency of the perturbation increase. It is suggested that the viscous eigenstates may be responsible for the excitation of some boundary-layer disturbances by disturbances in the free stream.

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.

A closed tube is considered in which the oscillations of a gas column are driven by the sinusoidal motion of a piston. The case where the frequency of the gas column in the tube lies near one of its resonant frequencies is of special interest. The aim of this paper is to extend the theory of Chester (1964), who has given solutions in the inviscid case and for very small boundary-layer friction, to cases of frictional effects of arbitrary strength. This is done by means of a combination of analytical and numerical methods. Different methods are applied for different strengths of the boundary-layer friction. The cases where the influence of the Stokes boundary layer is either very strong or very weak are not especially difficult to treat. The main part of this paper considers cases of intermediate friction, i.e. when the shock strength has grown rather small owing to the influence of the Stokes boundary layer. To obtain an overall view of the phenomena which occur in the Merent regions, a number of solutions have been calculated.