Measurements of time-mean velocity have been made in a flat channel (aspect ratio 12 to 28), one of whose walls consists of a belt which can be moved in the direction of air blown through the channel or in the opposite direction. The wall layers generated in twenty-six turbulent flows, including plane Poiseuille and plane Couette cases, are compared with analytical results obtained by Kader & Yaglom and by Townsend. Empirical descriptions are developed for the viscous, logarithmic and gradient portions of these wall layers. The core regions of both Couette-type and Poiseuille-type flows are also described empirically. Parallels are drawn with developing boundary layers, and phenomena are identified that relate to the relaminarization of boundary layers.

A series of experiments is described in which a fully-submerged circular duct situated with its axis vertical is subjected to regular incident waves. The resulting wave-interaction effects are defined in terms of reflexion coefficients derived from waveheight measurements, and a pressure coefficient derived from measurements of pressure in the depths of the enclosure. The experiments were conducted in a wide tank, so simulating open-sea conditions, and in a narrow tank where wall effects were important. The particular case when a transverse standing wave was induced above the duct was examined in detail.

These three-dimensional experiments complement a previous investigation into the performance of two-dimensional ducts and are of current practical significance in the context of sub-sea wave-energy conversion.

A study has been made of the flow past thin, inflated lenticular aerofoils at zero angle of incidence. The configuration is an idealization of the flow past long low inflated buildings when the effects of the earth's boundary layer are neglected. It is shown theoretically, and confirmed experimentally, that the non-dimensional tension coefficient in the inflated membranes comprising the aerofoil is a unique function of the internal pressure coefficient divided by the square root of the excess-length ratio. This applies for excess length ratios up to at least 0·05 which corresponds to a thickness-to-chord ratio, wind off, of 0·28. The aerofoil is found to become unstable at negative internal pressures corresponding to tension coefficients of approximately 0·4.

The theory has also been used to predict the shape of the aerofoil and the pressure distribution over it. With increasing wind speed at positive internal pressures, the membrane theoretically changes shape from a circular arc to a form involving inflexion points and in all cases the contours are symmetrical about the half-chord point. The non-dimensional membrane slope at the leading and trailing edges agrees fairly well with the experimental values. However, the measured pressure distributions show some fore-and-aft asymmetry and the maximum thickness is slightly downwind of the half-chord point. Nevertheless the comparison between theory and experiment is satisfactory for small values of the excess-length ratio.

Using automated laser-Doppler methods we have identified four distinct sequences of instabilities leading to turbulent convection at low Prandtl number (2·5–5·0), in fluid layers of small horizontal extent. Contour maps of the structure of the time-averaged velocity field, in conjunction with high-resolution power spectral analysis, demonstrate that several mean flows are stable over a wide range in the Rayleigh number R, and that the sequence of time-dependent instabilities depends on the mean flow. A number of routes to non-periodic motion have been identified by varying the geometrical aspect ratio, Prandtl number, and mean flow. Quasi-periodic motion at two frequencies leads to phase locking or entrainment, as identified by a step in a graph of the ratio of the two frequencies. The onset of non-periodicity in this case is associated with the loss of entrainment as R is increased. Another route to turbulence involves successive subharmonic (or period doubling) bifurcations of a periodic flow. A third route contains a well-defined regime with three generally incommensurate frequencies and no broadband noise. The spectral analysis used to demonstrate the presence of three frequencies has a precision of about one part in 104 to 105. Finally, we observe a process of intermittent non-periodicity first identified by Libchaber & Maurer at lower Prandtl number. In this case the fluid alternates between quasi-periodic and non-periodic states over a finite range in R. Several of these processes are also manifested by rather simple mathematical models, but the complicated dependence on geometrical parameters, Prandtl number, and mean flow structure has not been explained.

An exact solution of the nonlinear magnetohydrodynamic equations for a viscous incompressible fluid of finite conductivity is obtained, which represents a circularly polarized structure with time dependent amplitude in a uniform magnetic field. There is a phase difference of ½π between the spatial structures of the velocity and the magnetic field of the disturbance. In the inviscid perfectly conducting limit, this solution represents a standing helical oscillation which is a circularly polarized standing Alfvén wave of arbitrary amplitude, and the sum of the kinetic and magnetic energy densities of the oscillation are constant in the absence of any input of energy.

The mixing produced by dropping a horizontal grid through a sharp density interface is examined experimentally. The fraction of the available kinetic energy used to mix the fluid, the flux Richardson number Rf, is measured as a function of the overall Richardson number Ri0. It is found that Rf increases from zero as Ri0 does, reaches a maximum, and then decreases with further increase in Ri0. The final interface thickness is found to be a decreasing function of Ri0, and the equivalent vertical diffusion coefficient is calculated. Qualitative observations of the flow show that the final stages of the decay of motion in the interface are characterized by pancake-shaped modes with large horizontal and small vertical scales.

The presence of discontinuities in the Strouhal-number–Reynolds-number relationship was observed in several flows for cylinders in the Reynolds-number range 50–175. An experimental technique was devised to monitor carefully the shedding frequency and free-stream velocity so that the transitions could be distinctly observed. Quantitative Strouhal-number–Reynolds-number data, for cylinders of length-to-diameter ratio exceeding 150, agree reasonably well with the results of Tritton (1959) and Berger (1964).

This paper reports on an extensive experimental study of the flows due to under-expanded axisymmetric jets impinging on flat plates. The range of plate locations extends to a point where the jet is just subsonic but the main emphasis is on the behaviour in the first shock cell. Plate inclinations from 90° to 30° were investigated by means of comprehensive surface pressure measurements and shadowgraph pictures. Wherever possible, the main features of the results have been reconstructed using inviscid analyses of the wave interactions.

The flows are shown to be extremely complex due to the local structure of the free jet and, particularly, due to interactions between shock waves in the free jet and those created by the plate. In the near field, these interactions tend to be the controlling factors but at larger distances from the nozzle, mixing effects become increasingly important.

The maximum pressure on the plate when it is inclined can be very much larger than when the plate is perpendicular, owing to the possibility of high pressure recoveries through multiple shock systems. Correlations are presented for some of the main features on perpendicular plates and it is shown that the integrated pressure loads for both normal and inclined plates can be predicted well by a simple momentum balance.

A variational expression is constructed for the drag on a sphere of radius a that moves with speed U [Lt ] Ωa along the axis of a container of rotational speed Ω and length h [Gt ] a with E = v/Ωa2 [Lt ] 1. Two complementary approximations, based on the asymptotic solutions in the limits δ = Eh/2a ↑ ∞ and δ ↓ 0, and a variational interpolation between these approximations are compared with the numerical results of Hocking, Moore & Walton (1979). The limit δ ↓ 0 is singular, and the variational principle fails in that limit in the sense that the error in the drag is of the same order as the error in the trial function rather than of second order therein; nevertheless, the variational interpolation is in error by less than 0·1% for δ > 0·003 and by less than 1% for all δ. The variational formulation may be of interest in other contexts.

Fully developed oil flow in a smooth circular pipe at a mean Reynolds number of about 2100 was subjected to a nominally sinusoidal flow modulation at frequencies ranging from 0·05−1·75 Hz. It was observed that flow oscillation increased the critical Reynolds number and, under certain conditions, even brought about laminarization of the flow, which would be intermittently turbulent at the mean Reynolds number under quasi-steady (infinitely small oscillation frequency) conditions. The occurrence and extent of laminarization was, however, found to depend on factors such as the intermittency of turbulent puffs in the mean quasi-steady flow, frequency of oscillation, etc. Two series of experiments were performed. In one series, the oscillatory flow was almost completely laminarized. In the other series, the oscillatory flow was fully turbulent. In both the cases, instantaneous velocities in the flow were measured using laser-Doppler anemometry (LDA). The instantaneous velocity was decomposed into time-mean, periodic and random components employing ensemble-averaging techniques. The experiments indicated that the laminarized oscillatory flow behaves very similarly to laminar oscillatory flow at either end of the Strouhal-number range studied. The oscillatory turbulent flow was found to depend on both the Strouhal number and the ratio of the oscillation frequency (f) to some characteristic frequency (ft) of turbulence in the flow. The design of the present experimental facility made it possible to study the flow at f/ft ≈ 1 (‘high’ oscillation frequency), a condition that could not be attained in most previous investigations. Another unique feature of the present experiment was that the viscous sublayer and Stokes layer were both large enough (several millimetres in thickness) to allow detailed measurements to be made in these regions. It was found, that at this high frequency of oscillation, the Reynolds stresses generally remained frozen at an average state during the entire oscillation cycle. The turbulent structure showed significant departures from equilibrium at all times during the oscillation cycle. As a result, there was a net change in the time-mean velocity profile near the wall and a net increase in the time-mean wall shear stress and power loss due to friction. The observation that unsteadiness can indeed affect the mean flow behaviour in a significant way is new and contradicts the view presently held by many researchers (based on their studies at relatively low oscillation frequencies, i.e. f/ft [Lt ] 1). The data also indicated that the direct interaction between oscillation and the turbulent structure was essentially confined to the Stokes layer. The study suggests that (again contrary to the existing belief) quasi-steady turbulence models may not be adequate to describe unsteady flows when the time scale of unsteadiness is comparable to that of dominant turbulent eddies.

The role of large vortex structures in the evolution of a two-dimensional shear layer is studied numerically. The motion of up to 4096 vortices is followed on a 256 × 256 grid using the cloud-in-cell algorithm. The scaling predictions of self-preservation theory are confirmed for low-order velocity correlations, although the existence of vortex structures produces large fluctuations even in a simulation of this size. The simple picture of the shear layer as a line of vortex blobs, that merge pairwise thus thickening the layer, is not seen. On the contrary, the layer seems to thicken by the scattering of vortex structures of roughly fixed size about the midline. The size of the vortex structures does not scale with the layer thickness. A study of the entrainment of a passive marker shows that flow visualization experiments may have overestimated the size of the vortex structures. It appears that the finite area vortices have time to equilibrate between mergings, and the consequences of applying equilibrium statistical mechanics to their internal structure are explored. A simple model is presented which demonstrates how the size and separation of vortex structures may lock into a fixed ratio. This is precisely the type of mechanism that is needed to produce simple scaling in a flow that has initially several distinct length scales. A number of consistency checks on the numerical results are performed. In particular, the evolution of the same vortex configuration on two grids of different size is compared. This test showed that, although errors on subgrid scales do propagate to small wavenumbers, the dominant wavenumber of vorticity cascades back ahead of the peak in the error spectrum.

Exploratory measurements to study transport mechanisms in turbulent spots have been made using a passive temperature-tagging technique. Temperature fluctuations were measured on the centre-plane of spots artificially generated in the laminar boundary layer on a fully heated flat plate. The fluid near the wall is cooled and fluid far from the wall is heated during passage of the spot, with a more complex behaviour at intermediate locations. Contours of ensemble-averaged temperature disturbance measured relative to the laminar undisturbed profile show a region of maximum heating near the upper front of the spot and a region of maximum cooling at the rear of the spot near the wall, a structure strongly anti-correlated with corresponding contours of the longitudinal velocity disturbance as measured by Zilberman, Wygnanski & Kaplan (1977). The observed position of the upper heating maximum appears to be related to mean streamline pictures obtained by previous investigators in which streamlines entering the rear of the spot are deflected upward into the heated region. In conical similarity co-ordinates there is a near coincidence of the maxima and minima in the temperature disturbance contours with the two stable foci, or points of accumulation, for particle paths found by Cantwell, Coles & Dimotakis (1978), but the position of the hot core region cannot be explained in terms of the centre-line particle paths. An alternate viscosity-dependent scaling produces closer coincidence of the temperature and velocity disturbance extrema with the foci.

This paper presents a study of steady gravity currents entering a two-layer system, with the current travelling either along the boundary to form a boundary current, or between the two different layers to form an intrusion. It is shown that, at the front of an intrusion, the streamlines meet at angles of 120° at a stagnation point. For an energy-conserving current the volume inflow rate to the current, the velocity of propagation and the downstream depths are determined. In contrast to the pioneering study of Benjamin (1968), it is found that the depth of the current is not always uniquely determined and it is necessary to use some principle additional to the conservation relationships to determine which solution occurs. An appropriate principle is obtained by considering dissipative currents. In general, if the volume inflow rate to a current is prescribed, the current loses energy in order to maintain a momentum balance. We thus suggest the criterion that the energy dissipation is a maximum for a fixed volume inflow rate. It is postulated that the energy which is lost will go to form a stationary wave train behind the current. A nonlinear calculation is carried out to determine the amplitude and wavelength of these waves for intrusions. Such waves have been observed on intrusions in laboratory experiments and the results of the calculation are found to agree well with the experiments. Similar waves have not been observed on boundary currents because the resulting waves have too much energy and break.

In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.

The thickness of the entrainment zone, relative to the depth of the well-mixed layer just beneath, is found to be quite substantial (0·2 to 0·4), and apparently decreases only asymptotically with increasing ‘overall’ Richardson number, Ri*. The thickness is not well predicted by parcel theory.

Extensive detrainment is found to occur within the entrainment zone, and adds to the difficulty in defining the position of the local interface between mixed-layer fluid and unmodified fluid.

For typical Ri* values occurring in the atmosphere, the dimensionless entrainment rate is found to be given satisfactorily by 0·25(Ri*)−1, although an $(Ri^{*})^{\frac{3}{2}}$ dependence cannot be ruled out by the present data. Entrainment into a neutral layer in the absence of a capping inversion is found to proceed at the expected rate.

The self-similar motion of a polytropic gas with a linear velocity distribution is considered in an arbitrary ν-dimensional space. It is shown that if the initial state of the gas is isotropic the flow has a characteristic ellipsoidal form. Both expanding and compressing flows are shown to exist. The application of such flows as models for the expansion of an initially uniform mass of gas into vacuum is considered by comparison with computationally modelled expansions in one-dimensional cylindrical and spherical geometries. It is found that the accuracy of the representation increases when the heating time is long compared with the characteristic time of expansion.

When a pipe, connected to reservoirs at both ends, is subjected to an oscillating compression and expansion, fluid is alternately squeezed into and out of the reservoirs, causing a considerable amount of dissipation. This and two other related geometries (involving a symmetrical channel, and a pair of circular disks) are analysed for their flow patterns and energy dissipation, as a function of frequency. It is found that, under certain circumstances, the impedance due to transverse flow can greatly exceed the acoustical impedance (due to longitudinal flow).

A technique for measuring velocity gradients in laminar flows by homodyne light scattering is presented. A theory which describes the light-scattering spectrum is derived that includes the effects of different types of linear flow fields, particle diffusion and the intensity profile in the scattering volume. The conditions which must be satisfied in order that the theory describe the experimental situation are outlined and complementary experiments are performed which both verify the theory and apply the technique. Verification is provided using the flow in a Couette device, and the flow due to single rotating cylinder in a large bath of fluid. The technique is then applied to measure the spatial variation of the shear rate in a four-roll mill.

A new definition of concentration fluctuations in turbulent flows is proposed. The definition implicitly incorporates smearing effects of molecular diffusion and instrumental averaging. A stochastic model of two-particle dispersion, consistent with this definition, is formulated. The stochastic model is an extension of Taylor's (1921) model and is consistent with Richardson's $\frac{4}{3}$ law. Its predictions of concentration fluctuations are contrasted with predictions based on a more usual one-particle model.

The present model is used to predict fluctuations in three case studies. For example (case (i) of § 6), downstream of a linear concentration gradient we find $\overline{c^{\prime 2}}=\frac{1}{2}m^2(\overline{Z^2}-\overline{\Delta^2})$. Here m is the linear gradient, $\overline{Z^2}$ is related to centre-of-mass dispersion and $\overline{\Delta^2}$ is related to relative dispersion (see equation (3.1)). The term $\frac{1}{2}m^2\overline{Z^2} $ represents net production of fluctuations by random centre-of-mass dispersion, whereas $\frac{1}{2}m^2\overline{\Delta^2} $ represents net destruction of fluctuations by relative dispersion. Only the first term is included in the usual one-particle model (Corrsin 1952).

We consider the free-convective flow from a heated sphere, in the Boussinesq approximation, at high Grashof number. The characteristics of the boundary layer close to the surface of the sphere are evaluated numerically, and the eruption of the fluid from the boundary layer into the plume above the sphere is discussed.

The problem of transient natural convection in a cavity of aspect ratio A [les ] 1 with differentially heated end walls is considered. Scale analysis is used to show that a number of initial flow types are possible, collapsing ultimately onto two basic types of steady flow, determined by the relative value of the non-dimensional parameters describing the flow. A number of numerical solutions which encompass both flow types are obtained, and their relationship to the scale analysis is discussed.