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 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 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.

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.

A numerical model is proposed for the flow in a deep turbulent boundary layer over water waves. The momentum equations are closed by the use of an isotropic eddy viscosity and the turbulent energy equation. For small amplitudes the results are similar to those of Townsend's (1972) linear model, but nonlinear effects become important as the ratio of wave height to wavelength increases. With uniform surface roughness zo, the predicted fractional rate of energy input per radian advance in phase, ζ, decreases slightly with increasing amplitude and is of the same order of magnitude as in Miles’ (1957, 1959) and Townsend's linear theories. If zo is allowed to vary with position along the wave, however, the fractional rate of energy input can be significantly increased for small amplitude waves. If the variation in zo is half the mean value and the maximum wave slope zak is 0.01, we find ζ ≈ 60 (ρair/ρwater) (uo/c)2, where uo is the friction velocity and c the wave phase speed. Comparison is also made with recent laboratory and field data.

A new approximate theory is proposed for treating the flow past smoothly contoured two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < 0(102), where the displacement effect of the thick viscous layer near the surface of the body is large and a steady laminar wake is present. The theory is based on a new pressure hypothesis which enables one to take account of the displacement interaction and centrifugal effects in thick viscous layers using conventional first-order boundary-layer equations. The basic question asked is how the wall pressure gradient in ordinary boundary -layer theory must be modified if the pressure gradient along the displacement surface using the Prandtl pressure hypothesis is to be equal to the pressure gradient along this surface using a higher-order approximation to the Navier-Stokes equation in which centrifugal forces are considered. The inclusion of the normal pressure field with displacement interaction is shown to be equivalent to stretching the streamwise body co-ordinate in first-order boundary-layer theory such that the streamwise pressure gradient as a function of distance along the original and displacement body surfaces are equal.

While the new theory is of a non-rigorous nature, it yields results for the location of separation and detailed surface pressure and vorticity distribution which are in remarkably good agreement with the large body of available numerical Navier-Stokes solutions. A novel feature of the new boundary-value problem is the development of a simple but accurate approximate method for determining the inviscid flow past an arbitrary two-dimensional displacement body with its wake.

The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec = 88.53 and rotation number Ro = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro < 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.

A simplified theoretical model of a collapsing mixed region in a stably stratified fluid, as studied experimentally by Wu (1969), is presented. Unlike previous work the model describes the mixed region itself in the ‘principal stage’ of collapse. An inertia-buoyancy balance assumption is invoked, resulting in good quantitative agreement with Wu's results.

A surface-wave/internal-wave mode coupled model is constructed to describe the energy transfer from a linear surface wave field on the ocean to a linear internal wave field. Expressed in terms of action-angle variables the dynamic equations have a particularly useful form and are solved both numerically and in some analytic approximations. The growth time for internal waves generated by the resonant interaction of surface waves is calculated for an equilibrium spectrum of surface waves and for both the Garrett-Munk and two-layer models of the undersea environment. We find energy transfer rates as a function of undersea parameters which are much faster than those based on the constant Brunt-ViiisSila model used by Kenyon (1968) and which are consistent with the experiments of Joyce (1974). The modulation of the surface-wave spectrum by internal waves is also calculated, yielding a ‘mottled’ appearance of the ocean surface similar to that observed in photographs taken from an ERTS1 satellite (Ape1 et al. 1975b).