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The perturbation of a turbulent flow by an organized wavelike disturbance is examined using a dynamical, rather than phenomenological, approach. On the basis of the assumption that an infinitesimal perturbation results in a linear change in the statistics of the turbulence, and that the turbulence is either weak or that the turbulent perturbations are quasi-Gaussian, a method for predicting the perturbation turbulent Reynolds stresses is developed. The novel aspect of the analysis is that all averaging is delayed until the dynamical equations have been solved rather than attempting to find, apriori, equations for averaged quantities. When applied to long-wave perturbations the analysis indicates that the perturbation shear stress is of primary dynamical importance, and that this stress is determined by the principal component of mean shear through a relation which depends on the spectrum of the turbulent velocity component parallel to the gradient of the undisturbed mean velocity (the component perpendicular to the wall in a turbulent boundary layer). Theoretical arguments and observations are used to estimate the form of this spectrum in a constant stress shear layer. This results in a prediction of the constitutive law relating turbulent stress and the mean flow. The law is visco-elastic in nature, and is in agreement with the known constitutive relation for stress perturbations to a constant stress boundary layer; it resembles the eddy viscosity relation used successfully by others in describing perturbations in turbulent flows. The details of the constitutive law depend on how well the turbulence obeys Taylor's hypothesis that phase velocity equals mean flow velocity, and some insight into this question is given.

It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth's rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann's (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.

A simple model is proposed for the creeping motion of a bubble contaminated with an “insoluble” surface-active agent. The existence of a stagnant cap over the rear of the bubble is taken for granted, and the cap size and associated bubble drag are then computed theoretically, as functions of the surface pressure at which the contaminant film collapses. The model, which employs no adjustable parameters, is consistent with experimental observations and, in particular, explains the success of the empirical correlation relating the bubble drag to the Bond number.

Two hypotheses concerning the turbulent flow over an infinitesimal-amplitude travelling wave are investigated. One hypothesis, originally made by Miles, is that the wave does not affect the turbulence and therefore the turbulent Reynolds stresses are dependent only on height above the mean wave surface. Alternatively, the proposal that turbulent stresses are primarily dependent on height above the instantaneous wave surface is examined. Numerical solutions of the appropriate equations are compared with Stewart's recent experimental results and with the approximate solutions employed by Miles and others. No definite conclusion can be reached from comparison with experimental results since the predicted flows are quite sensitive to details of the mean velocity profile near the wave surface where no data was taken. It is found that the asymptotic results do not apply for the conditions investigated.

The two-dimensional stratified flow over an obstacle placed in a channel of finite height is examined to determine the extent to which Long's model provides an adequate description of real flows. A simple numerical method of solving Long's model for obstacles of arbitrary shape is used to calculate predicted streamline patterns which are compared with experimental observations of the flow over two bluff obstacles. If only a few lee-wave modes are excited there is qualitative agreement between theory and experiment, but, if the flow is subcritical with respect to several lee-wave modes, the effects of turbulence become dominant and the inviscid model is no longer useful. The theory predicts that the drag on an obstacle can increase with decreasing speed owing to the momentum transfer to lee-wave motion. Direct measurement of drag indicates that there are conditions under which the drag does increase with decreasing speed, but under these conditions the wake is dominated by turbulence and no lee waves can be detected.

The importance of fluctuating turbulent stresses in the flow over a wave is examined. It is shown that anisotropic stresses, which are most likely to be turbulent Reynolds stresses, are essential to the process of energy flow to the wave. Two fundamentally different methods of predicting fluctuating turbulent Reynolds stresses are examined. One method makes use of a phenomenological closure of the conservation equation for the turbulent Reynolds stresses and is similar to the turbulent boundary-layer calculation scheme of Bradshaw, Ferriss & Atwell (1967). The second method is based on the assumption that the turbulent stresses are determined by the recent history of velocity shear experienced by a fluid parcel and results in a viscoelastic constitutive relation for the turbulence; in the limit of shortest’ memory’ this relation becomes the eddy viscosity model proposed by Hussain & Reynolds (1970). Comparison of predicted and measured values of surface pressure indicates that the eddy viscoelasticity model can explain measured pressure distributions but the comparison is not conclusive. Suggestions for further measurements are made.

The nature of a shear flow over a wavy boundary of small amplitude is investigated. It is found that if the viscosity is small, the nature of the flow is highly dependent on the wave amplitude. If the wave amplitude is truly infinitesimal, the flow is described by the Orr-Sommerfeld equation and in the neighbourhood of the critical layer viscous stresses are important even in the limit of vanishing viscosity. However, if the wave is sufficiently large, viscous stresses may be neglected even in the critical layer. An approximate solution of the inviscid equations of motion is obtained to describe the flow over a small but finite wave in the limit of infinite Reynolds number.

A new type of solitary wave motion in incompressible fluids of non-uniform density has been investigated experimentally and theoretically. If a fluid is stratified in such a manner that there are two layers of different density joined by a thin region in which the density varies continuously, this type of wave propagates along the density gradient region without change of shape. In contrast to previously known solitary waves, these disturbances can exist even if the fluid depth is infinite. The waves are described by an approximate solution of the inviscid equations of motion. The analysis, which is based on the assumption that the wavelength of the disturbance is large compared with the thickness, L, of the region in which the density is not constant, indicates that the propagation velocity, U, is characterized by the dimensionless group (gL/U2) In (ρ1/ρ2), where g is the gravitational acceleration and ρ is the density. The value of this group, which is dependent on the wave amplitude and the form of the density gradient, is of the order one. Experimentally determined propagation velocities and wave shapes serve to verify the theoretical model.