Plane turbulent mixing between two streams of water which contained dilute chemical reactants was studied in a new blow-down water tunnel. In a diffusion-limited reaction, a pH indicator, phenolphthalein, in one stream mixed and reacted with a base, sodium hydroxide, in the other stream to form a visible reaction product. The product was found to exist, as expected, in concentrated regions associated with the large, span-wise-coherent structures of the turbulence. A transition in the mixing was observed in which the aqueous mixing product increased by an order of magnitude. The transition is a consequence of the appearance and development of small-scale three-dimensional motions in the flow. Downstream of the transition, the amount of mixing product was independent of Reynolds number (for an order-of-magnitude increase in the latter) and at most only weakly dependent on Schmidt number.

We have studied the transition between oscillatory and steady convection in a simplified model of two-dimensional thermosolutal convection. This model is exact to second order in the amplitude of the motion and is qualitatively accurate for larger amplitudes. If the ratio of the solutal diffusivity to the thermal diffusivity is sufficiently small and the solutal Rayleigh number, RS, sufficiently large, convection sets in as overstable oscillations, and these oscillations grow in amplitude as the thermal Rayleigh number, RT, is increased. In addition to this oscillatory branch, there is a branch of steady solutions that bifurcates from the static equilibrium towards lower values of RT; this subcritical branch is initially unstable but acquires stability as it turns round towards increasing values of RT. For moderate values of RS the oscillatory branch ends on the unstable (subcritical) portion of the steady branch, where the period of the oscillations becomes infinite. For larger values of RS a birfurcation from symmetrical to asymmetrical oscillations is followed by a succession of bifurcations, at each of which the period doubles, until the motion becomes aperiodic at some finite value of RT. The chaotic solutions persist as RT is further increased but eventually they lose stability and there is a transition to the stable steady branch. These results are consistent with the behaviour of solutions of the full two-dimensional problem and suggest that period-doubling, followed by the appearance of a strange attractor, is a characteristic feature of double-diffusive convection.

Lagrangian statistical results are presented from numerical simulations of an ensemble of fluid particles which were generated from a two-dimensional pseudospectral code. The single-particle results are in qualitative agreement with previous simulations on a lower-resolution grid. The two-particle, relative velocity correlations were found to fall off more rapidly than the single-particle correlations for short to intermediate times due to large-scale eddy advection in the single-particle case. The temporal behaviour of the mean square relative separation, 〈rl2〉, is analysed for short to intermediate times and is found to be consistent with scaling arguments based on Kraichnan's expression for the non-local strain acting in the high-wavenumber enstrophy cascade spectral range. For longer times, 〈rl2〉 exhibits tn behaviour. The power-law region is associated with the locally determined strain rates which characterize a backward energy-cascade spectrum.

The ‘numerically exact’ properties of plane periodic deep-water waves are used in a slowly-varying-wave approximation for a steady axisymmetric wave field. The linear ‘ray’ theory for such a wave field corresponds to waves approaching a circular caustic. A parameter, C, characterizes each solution. If C is smaller than 20 the wave behaviour is dominated by the convergence of wave energy and waves are expected to break. Comparison with experiment for C = 0 indicates that breaking may be accurately predicted. If C is greater than 50 then the waves propagate closer to the caustic and, since it is of Peregrine & Smith's (1979) type R, it is likely that the waves do not break. These solutions show that wave action does not flow along the straight lines of the linear rays.

A study has been made of the effects of non-axisymmetric bottom topography in a differentially heated, rotating fluid annulus. In the absence of free baroclinic waves the disturbance produced by topography of vertical dimensions typically much less than the depth of the fluid and horizontal dimensions comparable to the gap width is steady and confined to the lower part of the fluid. The maximum amplitude of this disturbance depends on the angular speed of rotation of the apparatus and varies with height, being very small above the level where the basic azimuthal flow reverses. The flow pattern shows a closed circulation displaced relative to the topography in the downstream direction. In the presence of free baroclinic waves the topographic wave extends throughout the whole depth of the fluid. Determinations of the amplitude and phase of the various azimuthal Fourier components present show that the topographically forced components exchange energy with the free components as they drift relative to the topography.

Measurements of Rayleigh numbers R and Nusselt numbers N have been made for a cylindrical cell having a radius to height ratio of 4·72 and containing liquid helium I. The upper surface of the cell was maintained at a constant temperature T2 near T0 = 2·178 K where the fluid density has a maximum. The heat input to the cell bottom was varied quasi-statically while the lower surface temperature T1 was recorded. The penetration parameter [Pscr ]≡(T1−T2)/(T1−T0) ranged between 0·1 and 3 for our experiments.

For [Pscr ] < 1, the initial slope of N(R) for R near the critical Rayleigh number Rc was independent of [Pscr ]. For ${\cal P}\;{\mathop {\raise-2pt\hbox{$>$}}\limits^{\raise-8pt\hbox{$\sim$}}}\;1$, two hysteresis loops of N(R) were observed. One of them occurred very near Rc and is interpreted in terms of the inverted bifurcation associated with the onset of cellular convection of non-Boussinesq systems. The other, for R > Rc, is believed to correspond to the transition from cellular to two-dimensional flow. Near Rc and with [Pscr ] > 2 we also observed multistability, with the states believed to correspond to different numbers of convective cells.

For large [Pscr ] the onset of time-dependent flow occurred much closer to Rc than is the case for Boussinesq systems.

The gravity-wave scattering matrix for a barrier reef that separates two different depths of water is calculated by an extension of a variational analysis of diffraction by a discontinuity in depth (Miles 1967). The resulting transmission coefficient for equal depths differs from that obtained by Johnson, Fuchs & Morison (1951), which appears to be incorrect. The results are applied to the calculation of resonant amplification of incoming swell or tsunamis by a shallow lagoon that is bounded by the reef and a vertical inner boundary. The results for this last problem agree closely (exactly for equal depths) with those obtained by Tuck (1980) through a rather different approach.

This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.

We study the motion which results when a fluid film is squeezed between two parallel plane surfaces in relative motion. Particular attention is given to the special case where one surface is fixed and the other is rapidly accelerated from a state of rest to a state of uniform motion. The analysis is based in part on linear theory and in substance on a finite-difference analysis of the full nonlinear equations of motion.

Experiments are described in which a radial temperature gradient is maintained along the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical side walls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby (1965) and the same general asymmetric circulation is observed, i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base.

A boundary-layer scaling analysis demonstrates the existence of six flow regimes, depending on the magnitude of a quantity Q defined such that Q is the square of the ratio of the (non-rotating) thermal-layer scale to the Ekman-layer scale. For small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer. Also presented are some numerical similarity solutions for the special case of a quadratic temperature distribution on the lower boundary and partially covering the range of Q achieved in the experiments, which is zero to ten. Above a certain critical value of Q (for the geometry used here Qc = 3·4) a baroclinic wave regime exists but is not examined in detail here although a brief discussion of an instability problem is given. Throughout comparisons are drawn between the experimental results and theoretical aspects of the problem.

It is thought that the essential features of a system thermally driven in this way have their counterparts in natural systems such as the large-scale thermally induced ocean circulation driven by the latitudinal variation of incoming solar radiation.

The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.

Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.

The nonlinear stability of a thermally stabilized horizontal plane layer of dielectric liquid subjected to unipolar charge injection at a voltage near the linear instability threshold is investigated using a normal-mode cascade analysis valid for small perturbation amplitudes. In this first analysis, the primary mode is chosen to be a system of parallel rolls whose amplitude varies aperiodically with time. The branching behaviour at the critical voltage is found to reflect the distinction, apparent in the linear instability problem, between an essentially isothermal space-charge instability and an instability dominated by the effects of an ion mobility varying with temperature. The effect of motion on heat and charge transfer through the system is also considered. Furthermore, in certain cases it appears that overstability is the preferred form of linear instability.

The influence of surface roughness on the vortex-shedding frequency in the wake of a single cylinder has been investigated. The experiments were carried out in an atmospherical and a high-pressure wind tunnel. The tests were started with a smooth cylinder. Then the wake flow of cylinders with relative roughnesses of ks/d = 75 × 10−5, 300 × 10−5, 900 × 10−5, and 3000 × 10−5 was investigated.

For all roughness parameters tested the Strouhal number exhibited an increase in the critical flow regime. With growing roughness parameter the step in the curve became smaller. At transcritical flow conditions the Strouhal number was measured to be in the range of Sr = 0·25 ± 0·018 for all surface roughness tested. No regular vortex shedding could be observed in the critical flow range for the smooth cylinder with l/d = 3·38. When prolonging the test body to l/d = 6·75 the wake fluctuations became periodic.

In studying head-sea diffraction by a slender body via matched asymptotics, Haren & Mei (1981) found numerically that the normalized inner problem is singular at a special frquency. In the present note, this singularity is confirmed by a different numerical method and by an analytical demonstration in the shallow-water limit.

The purpose of this note is to clarify the discrepancy between the results of Cramer (1979), Barnwell (1975) and Cheng & Hafez (1975). These authors have all derived the boundary-value problem governing the flow far from a three-dimensional lifting wing in transonic flow. The results of both Cramer and Barnwell will provide the lowest-order solution in the far field. The results of Cheng & Hafez are not only accurate to lowest order but to first order as well. That is, the theory of Cheng & Hafez is an order-of-magnitude more accurate than those of Barnwell and Cramer. This is the reason for the discrepancy between the boundary condition derived by Cheng & Hafez and that of Cramer and Barnwell. Because Cheng & Hafez correctly derive the first-order results, the lowest-order theories of Cramer or Barnwell cannot correct those of Cheng & Hafez. It should be recognized that the main contribution of Cramer's work was to clarify the structure of the problem and to simplify the analysis rather than correct the basic results.

A numerical and experimental study has been made of the three-dimensional flow and heat transfer by natural convection in a closed, rectangular thermosyphon. At low Rayleigh numbers, the flows in the two halves of the cavity remain separate, with heat transfer across the mid-height plane occurring only by conduction. At increasing Rayleigh numbers, an exchange process of increasing complexity occurs. The numerical solutions were used to explore this process and to predict flow patterns which were found to resemble closely those observed during previous investigations of cylindrical thermosyphons. The results were verified by a flow visualization study. Heat-transfer rates are presented and augment previous data for higher values of the governing parameters.

A method is described for photographically recording the two-dimensional distribution of sugar concentration in a tank, which typically yields a resolution of 0·01 in weight fraction sugar. The tank image is coloured according to the sugar concentration, giving a quantitative visual record of sugar contours. The technique is demonstrated in photographs of a laboratory model of an oceanic front, in which interleaving quasi-horizontal layers are formed by double-diffusive effects.

The paper summarizes results from an experimental study of buoyancy-induced motion and heat transfer in a horizontal rectangular cavity with the two vertical ends at different temperatures and the long horizontal walls adiabatic. The cavity height/length ratio is A = 0·0625. The high-Rayleigh-number range reported on in this paper, 2 × 108 < Ra < 2 × 109, has not been studied before. It is shown that, contrary to lower-Rayleigh-number behaviour known previously, the core flow structure is non-parallel and is dominated by horizontal intrusions flowing along each of the two insulated horizontal walls of the enclosure. The fluid embraced by the two horizontal jets is practically stagnant and thermally stratified. Flow visualization experiments suggest that adjacent to the two horizontal jets two secondary flat cells are formed by the baroclinic pressure field in an analogous way to what is observed in intrusions in a stratified fluid. Nusselt-number-Rayleigh-number results for the overall end-to-end heat transfer in the horizontal direction are reported and compared with previous experimental and theoretical results available for lower Rayleigh numbers. It is shown also that the transition from a parallel core structure to one dominated by intrusion layers is governed by the parameter Ra½A, with Ra¼A < 1 as necessary condition for a parallel core flow.

The study of nonlinear magnetosonic waves in a turbulent plasma is extended to include the effects of the Hall term. The turbulence and Hall effect are characterized by an effective electrical conductivity and an ion gyrofrequency respectively. It is shown that the magnetosonic waves are governed by a nonlinear equation which can be considered as the generalization of a Korteweg & de Vries (1895) equation with dispersion. For a stationary solution two cases are considered in detail: (a) an unperturbed magnetic field is almost parallel to a wave vector, and (b) they are almost perpendicular. In the case (a) it is shown that the presence of the Hall term can lead to an oscillatory solution which decays due to the finite conductivity. In the second case the Hall effect does not affect the monotonous character of a decaying Taylor-shock profile.

This study continues the investigation of particle motions near the bottom in a turbulent open channel flow, reported by Sumer & Oguz (1978; hereafter referred to as part 1). Paths of suspended heavy particles were recorded in three dimensions and in time, employing a stereo-photogrammetric system coupled with a stroboscope. In the case of smooth bottom, the measured kinematical quantities concerning the particle motions were found to be in accord with the available information on the ‘bursting process’. Agreement between the particle motion and the bursting process provided further support for the mechanism of particle suspension near the bottom proposed in part 1. Similar experiments were carried out when the bottom was rough. Comparison between the smooth- and rough-bottom cases could be made on the same basis as the flow Reynolds number as well as the particle properties were kept almost unchanged in both the smooth and rough boundary experiments. The observations showed that particle motions close to the rough bottom are very similar in character to those in the smooth-bottom case. The findings of the present paper suggested that the suspension mechanism given for the smooth-boundary flow could be extended to the rough-boundary case.