Equations governing the current system in the upper layers of oceans and lakes were derived by Craik & Leibovich (1976). These incorporate the dominant effects of both wind and waves. Solutions comprising the mean wind-driven current and a system of ‘Langmuir’ cells aligned parallel to the wind were found for cases in which the wave field consisted of just a pair of plane waves. However, it was not clear that such cellular motions would persist for the more realistic case of a continuous wave spectrum.

The present paper shows that, in the latter case, infinitesimal spanwise periodic perturbations will grow on account of an instability mechanism. Mathematically, the instability is closely similar to the onset of thermal convection in horizontal fluid layers. Physically, the mechanism is governed by kinematical processes involving the mean (Eulerian) wind-driven current and the (Lagrangian) Stokes drift associated with the waves. The relationship of this mechanism to instability models of Garrett and Gammelsrød is clarified.

The propagation of hydromagnetic planetary waves in a rotating thin shell of fluid in regions of magnetic and velocity shears is studied using the β-plane approximation. In slowly varying shear the use of the WKBJ approximation makes it possible to construct the various types of ray trajectory that can occur and consequently the conditions that give rise to critical-latitude phenomena and trapping are deduced.

The opposite extreme to the WKBJ limit, namely reflexion and refraction of waves by a current-vortex sheet, is also analysed. In this case the conditions that lead to wave amplification (or over-reflexion) are investigated. Qualitatively, it is found that reflected Alfvén modes are amplified if the jump in the flow speed across the sheet lies between two speeds which are respectively greater and less than the sum of the Alfvén speeds on either side of the sheet. Also, Rossby waves incident upon a sufficiently strong easterly flow can suffer over-reflexion.

The general case of reflexion and refraction at a finite double (magnetic and velocity) shear layer is discussed. In analogy with the invariance of ‘wave action’ of gravity waves in a shear flow we construct a quantity [Ascr ] which is invariant except at critical latitudes, where it is discontinuous. By using the asymptotic solutions near these critical latitudes and by adopting the proper matching procedure for the solutions on either side of these latitudes it is possible to relate the two constant values of [Ascr ] on either side of each critical latitude. These general results are then applied to various profiles of shear flow and magnetic field so as to elucidate the manner in which an incident wave is reflected from and transmitted through a double layer.

The steady movement of a liquid meniscus in a circular capillary tube has been examined theoretically for dynamic contact angles close to 90° with minute slippage of the liquid on the solid, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce an unbounded force at the contact line, contrary to that with the no-slip condition. The interfacial velocity, wall stress, fluid pressure and the meniscus shape are calculated, and the significance of dynamic contact-angle measurements is discussed. A modified version of the classical Washburn equation which takes account of the meniscus also reveals the importance of slippage.

A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.

The hydrogen-bubble technique has been used to measure the velocities of pulsating water flow in a rigid circular pipe. Mean flows with Reynolds numbers between 1275 and 2900 were superimposed on an oscillating flow produced by moving the pipe axially with simple harmonic motion. While the velocities in the oscillating boundary layers on the pipe wall were found to be close to those predicted by laminar flow theory, at the higher Reynolds numbers the velocities near the centre of the pipe were lower than those predicted and more uniformly distributed.

The intermittency of the periodic bursts of turbulent motion at the higher Reynolds numbers was measured. At each mean-flow Reynolds number the turbulent intermittency of the flow was found to be a function of a single parameter: the harmonicflow Reynolds number.

An integral technique suggested for the analysis of turbulent jets by Corrsin & Uberoi (1950) and Morton, Taylor & Turner (1956) is re-examined in an attempt to improve the description of the entrainment. It is determined that the hypothesis of Priestley & Ball (1955), that the entrainment coefficient is a linear function of the jet Richardson number, is reasonable, and that two empirically determined plume parameters are sufficient to describe the transition of buoyant jets to plumes. The results of a series of experiments in which both time-averaged velocity and time-averaged temperature profiles were recorded in a substantial number of plane turbulent buoyant jets of varying initial Richardson numbers are used to verify the basic ideas. In addition, measurements of the mean tracer flux in a series of buoyant jets indicate that as much as 40% of the transport in plumes is by the turbulent flux.

The effect of tube elasticity on the stability of Poiseuille flow to infinitesimal axisymmetric disturbances is investigated. The disturbance equations for the fluid are solved numerically while those for the arbitrarily thick tube are solved analytically in terms of Bessel functions of complex argument. It is shown that an elastic tube can cause instability of Poiseuille flow, unlike a rigid tube, in which the flow is always stable. Neutral curves are presented for various values of the tube parameters. It is found that the critical Reynolds number varies almost as the square root of the Young's modulus of the tube material while the critical dimensionless frequency is almost invariant, being about 1·1 for the cases studied.

The effects of gravity waves on wind-generated ripples are studied experimentally by means of Doppler spectra obtained through microwave Bragg backscattering. The measurements were made at 9·23 GHz with incidence angles of between 45° and 55°. It is found from the Doppler frequency shift that an increase in the speed of Bragg waves (ripples) of wavelength approximately 2 cm can be detected when a gravity wave is propagated into a pre-existing wind-wave field. The Doppler frequency shift corresponds, to first order, to the orbital speed of the gravity wave. Further studies, using a conditional sampling technique, reveal that the Bragg scatterers are localized on the gravity wave's crest. The mechanism leading to the ‘localization’ is as yet unidentified. Ratios of gravity wavelength to Bragg (ripple) wavelength ranging from 13 to 35 have been studied.

A conditioning function is generally used to discriminate between the turbulent and non-turbulent zones in intermittent flows. Any fluid-mechanical property is conditioned by multiplying it by the intermittency function. A formalism is developed in which some integrals of the fluid-mechanical variables at the interface are important ingredients with a precise physical meaning. The present ideas may prove to be useful in turbulence dynamics and turbulent mixing of scalars.

A linear stability analysis is presented for flow between concentric cylinders when a fully developed axial flow is present. Small perturbations are assumed to be nonaxisymmetric. This leads to an eigenvalue problem with four eigenvalues: the critical Taylor number, an amplification factor and two wavenumbers. The presence of the tangential wavenumber permits prediction of the stability of spiral flow. This made it possible to model the flow more accurately and to extend the range of calculations to higher axial Reynolds numbers than had previously been attainable. Calculations were carried out for radius ratios from 0·95 to 0·1, Reynolds numbers as large as 300 and cases with co-rotation and counter-rotation of the cylinders.

Results of experiments on capillary-wave decay and energy transfer to mean currents are presented. The conditions investigated were those of a progressive wave train propagating on still water, on a constant current and on a spatially varying current. The waves were generated by either a mechanical or a pneumatic wave maker and the wave maker usually excited cross-wave motion. Thus the study also provides data on cross-wave generation and growth under these conditions. In particular these results indicate that the cross-waves obtain energy from a constant current as well as a spatially varying current. The progressive-wave energy was separated from that in the cross-waves by spatial averaging. When this is done the wave-current interaction and wave decay can be described by a first-order theory which includes viscous dissipation.

The turbulence structure of a plane vertical buoyant jet in the transition state from jet-like to plume-like growth is the object of this investigation. The ambient fluid is of uniform density and motionless except for the flow induced by the jet.

An analysis of the turbulence energy equation reveals that the production of turbulent energy by the buoyancy forces relative to the production by the shear stress increases as the jet Richardson number increases, and becomes constant for a plume-like buoyant jet.

A systematic set of experiments was carried out to examine the turbulence structure for a wide range of initial Richardson numbers, extending from a value appropriate to a jet-like flow (very close to zero) to that appropriate for a plume-like flow (approximately 0·6). Fast-response thermistors and a laser-Doppler velocimeter were used to measure the buoyant jet's temperature and velocity respectively. The temperature and velocity data were recorded magnetically in digital form and subsequently processed to extract both mean and fluctuating values. The turbulence intensity and the probability density distribution of the temperature and velocity fluctuations, the maximum and minimum temperature, the intermittency, and the frequency of crossing of the hot/cold and the cold/hot interface of a buoyant jet were investigated. It was determined that the intensity of temperature and velocity fluctuations increases with increasing Richardson number. An explanation is suggested for the large-scale vortices observed in a plume.

Consider a background state which consists of a spatially uniform chemically reactive mixture in a general state of disequilibrium. The analytical method of characteristics is used to show that a plane finite amplitude disturbance propagates through this system at the frozen sound speed and, if the degree of disequilibrium is sufficient, is amplified by the chemical reaction. Some comments are made about the time to shock-wave formation and its relation to the homogeneous explosion ignition time, and also about expansion waves, which are found to have a tendency towards fixed-strength ‘quenching waves’, their strength being proportional to the extent of the ambient disequilibrium.

The initial-value problem for slightly viscous, two-dimensional, spatially periodic waves is examined. Matched asymptotic expansions in space for small wave amplitude a and multiple scales in time allow the boundary layers and viscous attenuation to be described. The bottom and surface boundary layers of thickness δ are equivalent to those of Longuet-Higgins except that wave attenuation is included. For progressive waves one solution for the interior motion independent of the magnitude of δ/a is an attenuating version of the conduction solution of Longuet-Higgins, but with modified structure, the O(a2) vorticity at the boundaries ultimately diffusing into the entire field. There are certain critical depths for which there is secular behaviour and these do not correspond to quasi-steady flows. Other solutions may be possible. For standing waves the interior flow depends on the magnitude of the steady-drift Reynolds number Rs∝ (a/δ)2 introduced by Stuart. When Rs [Lt ] 1, the interior is viscous with an O(a2) vorticity ultimately diffusing into the entire field. When Rs [Gt ] 1 there is a doubleboundary-layer structure on the bottom and on the surface. Within the outer layers, the O(a2) steady drift decays to the potential flow interior. A direct analogy with the flow structure on a circular cylinder oscillating along its diameter is introduced and pursued. Finally, all of the above fields are converted to Lagrangian fields so that masstransport profiles can be obtained. Comparisons are made with previous theoretical and experimental work.

The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.

The effect of a drag-reducing additive on the structure of wall turbulence in pipe flow was investigated experimentally. Real-time hologram interferometry was used for flow visualization and turbulence measurements. The real-time modulation of interference fringes by a refractive-index enhancer infused into the near-wall flow was recorded by medium-speed motion photography. The spanwise direction and the direction normal to the wall were studied to investigate the ‘streaks’ and ‘bursts’ that originate in the sublayer. A region of the flow was sampled for spatial and temporal correlations of concentration fluctuations to detect the scales of eddy interaction.

The addition of 50 p.p.m. by weight of Separan AP30 to water significantly altered the Newtonian wall-flow structure. The drag-reducing additive suppressed the formation of streaks and the eruption of bursts. When compared at the same wall shear, the sublayer period increased over the Newtonian value by a factor almost equal to the ratio of the corresponding non-dimensional streak spacings.

These results suggest a stabilized wall layer in the drag-reducing solution as compared with that of the Newtonian solvent, resulting in less turbulence production and reduced frictional drag. The role of the extensional viscosity of the dilute polymer solution is discussed as a possible mechanism for explaining the visualized and measured phenomena.

A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results. Starting at the beginning of the motion, at a nozzle, and proceeding downstream, these include the following.

1. A formation process that is strongly Reynolds number dependent.

2. The amount of vorticity that appears downstream is very close to that predicted by a simple ‘slug’ model. However flow-visualization studies show that such a model is an oversimplification and that an excess of ring vorticity is probably cancelled by the ingestion of vorticity of opposite sign at the nozzle lip.

3. (iii) A new, bimodal form of vortex-core instability has been observed at moderate but not high Reynolds numbers.

4. Azimuthal inhomogeneities in the breaking of these, and the normal instability waves, create an ‘axial’ flow along the vortex core in the turbulent ring. This axial flow takes the form of a propagating wave that has many characteristics of a solitary wave. It is hypothesized that this axial flow prevents further ring instability.

5. The long-term behaviour of the turbulent ring is marked by dramatic changes in its growth rate, which are probably related to changes in the ‘organization’ of the vortex core. The descriptive turbulent-ring model developed in Maxworthy (1974) is substantially confirmed by these experiments and by observation of ring propagation through a stratified ambient fluid.

We have observed two novel manifestations of the Weissenberg effect in viscoelastic liquids which are set into motion by the rotation of a circular rod. In the first experiment we floated a layer of STP on water. The STP climbs up the rod into the air and down the rod into the water. The ‘down-climb’ is much larger than the ‘up-climb’, their ratio being roughly the square root of the density difference (STP-air)/ (water–STP). The magnification of the down-climb may be regarded as normal-stress amplification. [dagger] The magnitudes of the up- and down-climbs are simultaneously in good agreement with the predictions of a theory of rod climbing when the angular frequency of the rod is small. In the second experiment, we set the rod into torsional oscillations. When the amplitude of the oscillation is small, the fluid climbs the rod; the climb is divided into an axisymmetric steady mean part and an oscillating part (Joseph 1976b; Beavers 1976). The mean axisymmetric climb dominates the total climb at low frequencies. At a higher critical speed the axisymmetric climbing bubble loses its stability to another time-periodic motion with the same period but with a ‘flower’ pattern displaying a certain integral number of petals.

This paper presents numerical results for the added-mass and damping coefficients of semi-submerged two-dimensional heaving cylinders in water of finite depth. A simple proof is given which shows that the added mass is bounded for all frequencies in water of finite depth. The limits of the added-mass and damping coefficients are studied as the frequency tends to zero and to infinity. A new formulation valid in the low-frequency limit is constructed by using a perturbation expansion in the wavenumber parameter. For the limiting cases, dual extremum principles are used, which consist of two variational principles: a minimum principle for a functional and a maximum principle for a different but related functional. These two functionals are used to obtain lower and upper bounds on the added mass in the limiting cases. However, the functionals constructed (Bai & Yeung 1974) for the general frequency range (excluding the limiting cases) have neither a minimum nor a maximum. In this case, the approximate solution cannot be proved to be bounded either below or above by the true solution. To illustrate these methods, the added-mass and damping coefficients are computed for a circular cylinder oscillating in water of several different depths. Results are also presented for rectangular cylinders with three different beamdraft ratios at several water depths.

A numerical investigation of the problem of rotating disks is made using the Newton–Raphson method. It is shown that the governing equations may exhibit one, three or five solutions. A physical interpretation of the calculated profiles will be presented. The results computed reveal that both Batchelor and Stewartson analysis yields for high Reynolds numbers results which are in agreement with our observations, i.e. the fluid may rotate as a rigid body or the main body of the fluid may be almost at rest, respectively. Occurrence of a two-cell situation at particular branches will be discussed.