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 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.

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.

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.

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 is concerned with steady flow in collapsible tubes, such as veins, at fairly low Reynolds number. Lubrication theory is used to calculate the velocity and pressure distribution in an elliptical tube whose cross-sectional area and eccentricity vary slowly and in a given way with longitudinal distance x. The transverse velocity field and the effect of inertia on the primary velocity and pressure distributions are calculated to first order in the relevant small parameter. The results of these calculations are combined with a relationship between transmural pressure and the cross-sectional area at any x which is close to that measured in (large) veins, and are used to predict the pressure and flow in a collapsible tube when a given distribution of external pressure is applied. Different relationships between the tube perimeter and cross-sectional area are examined. The theory is applied to an experiment in which a segment of collapsible tube is supported between two rigid segments, and squeezed; predictions of the relationship between the pressure drop and flow rate are made for various experimental conditions. In particular, when the resistance of the downstream rigid segment is held constant, a range of flow rates is found in which the pressure drop falls as the flow rate is raised; this agrees with experiment.

A finite-difference procedure for three-dimensional parabolic flows is used to predict the development of Taylor vortices in the flow between concentric rotating cylinders, resulting from the growth of small disturbances of a Couette flow. Predictions of such flows are presented in the developing and fully developed region. A precise calculation of the wavelength of the vortices has been possible by employing a periodic boundary condition on the pressure field. The predicted torque coefficient compares well with experimental data. The critical Taylor number has also been predicted with good accuracy.

Developing laminar flow in a liquid film issuing from a full slot and descending along a vertical wall is analysed for the limiting cases of low flow rate and high surface tension. Neither limiting case is approached uniformly and the singular perturbation method with matched asymptotic expansions is employed. The location of a free boundary, the curved meniscus, is unknown a priori, and the limiting meniscus profiles are obtained. An interesting viscous boundary layer is found at low flow rates.

This experimental investigation determines the effect of the various parameters of a subsonic axisymmetric jet upon a fast chemical reaction between ozone contained dilutely in the primary jet and diluted nitric oxide being entrained from the ambient fluid. Radial profiles of ozone densities are determined from absorption measurements of a thin beam of ultraviolet light which is probed across the jet. Data have been obtained for five jet Reynolds numbers between 4000 and 32 000 to reflect variations in both gas density and nozzle velocity; the data confirm Reynolds number independence of reactant concentration profiles to within experimental accuracy. When the non-dimensional chemical reaction rate exceeds a determined value, the ozone profiles are observed to be independent of further increases in the reaction speed. The measured ozone concentration profiles are related directly to the molecular-scale mixing in the jet and to mixing intermittency in the mixing zone in particular.

Experiments were conducted with two layers of stably stratified fluid in a wind-wave tank. The slope of the density interface was measured and was related to the wind stress, the density difference between the two fluids and the depth of the interface.

Two basins maintained at different densities are connected by a relatively shallow strait. If the strait is short, the flow is such that the Froude number is unity. The thickness of the intermediate layer, between the outflow and the inflow, is controlled by the requirement that the Richardson number be critical; this thickness is always about one-fifth of the total depth, both in these experiments and in the Strait of Gibraltar. If the strait is long, the Froude number is less than unity in the interior but increases to unity at each end. A strait may be considered short when its length is less than a few hundred times the sill depth.

This paper treats the steady inertialess flow of an incompressible viscous fluid through an infinite rectangular duct rotating rapidly about an axis (the y axis) perpendicular to its centre-line (the x axis). The prototype considered has parallel sides at z = ± 1 for all x, parallel top and bottom at y = ± a for x < 0 and straight diverging top and bottom at y = ± (a + bx) for x > 0. An earlier paper (Walker 1975) presented solutions for b = ±(1), for which the flow in the diverging part (x > 0) is carried by a thin, highvelocity sheet jet adjacent to the side at z = 1, the flow elsewhere in this part being essentially stagnant. The present paper considers the evolution of the flow as the divergence decreases from O(1) to zero, the flow being fully developed for b = 0. This evolution involves four intermediate stages depending upon the relationship between b and E, the (small) Ekman number. In each successive stage, the flow-carrying side layer in the diverging part becomes thicker, until in the fourth stage, it spans the duct, so that none of the fluid is stagnant.

Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.

The effect of helicity on the Lagrangian velocity covariance UL(t) in isotropic, normally distributed turbulence is examined by computer simulation and by a renormalized perturbation expansion for UL(t). The first term of the latter represents Corrsin's (1959) conjecture (extrapolated to all t), which relates UL(t) to the Eulerian covariance and the distribution G(x, t) of fluid-element displacement. Truncation of the expansion at the first term yields the direct-interaction approximation for G(x, t). The expansion suggests that with or without helicity Corrsin's conjecture is valid as t → ∞ and that in either case UL(t) behaves asymptotically like $t^{-(r+\frac{3}{2})}$ if the spectrum of the Eulerian field varies like kr+2 at small wavenumbers. Corrsin's conjecture breaks down at small and moderate t if there is strong helicity while remaining accurate at all t in the mirror-symmetric case. Computer simulations for a frozen Eulerian field with spectrum confined to a thin spherical shell in k space indicate that strong helicity induces an increase in the Lagrangian correlation time by a factor of approximately three. Direct-interaction equations are constructed for the Lagrangian space-time covariance and the resulting prediction for UL(t) is compared with the simulations. The effect of helicity is well represented quantitatively by the direct-interaction equations for small and moderate t but not for large t. These frozen-field results imply good quantitative accuracy at all t in time-varying turbulence whose Eulerian correlation time is of the order of the eddy-circulation time. In turbulence with weak helicity, the directinteraction equations imply that the Lagrangian correlation of vorticity with initial velocity is more persistent than UL(t), by a substantial factor.