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.

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).

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.

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.

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).

A theoretical model has been developed to investigate the stability of a disturbance in an incompressible turbulent shear flow dominated by turbulence scales that are small with respect to the cross-stream dimension of the flow. The approach utilizes the ‘phase average’ concept to derive the differential equations governing the mechanics of a potential flow disturbance. Turbulence closure is effected at second order. The result is an Orr–Sommerfeld-type equation with complications introduced by the turbulence model. Integration of the linear eigenvalue problem for a wake disturbance leads to the result that the critical eddy-viscosity-based Reynolds number is markedly increased by decreasing the turbulence scale. The viscoelastic behaviour of background turbulence, further complicated by the effects of mean shear, appears to provide stabilization and is discussed in some detail.

In part 1 (Woods 1979) generalized constitutive relations for the fluid stress p and the heat flux q were established by mean-free-path arguments. These relations are expected to hold over a wide range of Knudsen numbers K, but in the earlier paper, which presented the general theory, they were successfully tested only to O(K2), the order to which the Burnett constitutive equations are valid. It remains to verify the general theory at much higher K values, and to this end we have applied it to the propagation of forced sound waves in a rarefied monatomic gas.

Theories for such waves (based on the linearized Boltzmann equation) are available, and there are also experimental results for the speed and attenuation of waves up to K values of about 10. Our theory is in good agreement with experiment in the range 0 < K < 1. For K > 1 we obtain close agreement with experimental values of the wave speed, but as wave damping in this range is largely due to the unavoidable proximity of the wave transmitter – an effect not included in our calculations – we have found smaller values of the attenuation than obtaining in the experiments.

We study the initial-value problem posed by the small-amplitude (linearized) free oscillations of free drops, gas bubbles, and drops in a host liquid when viscous effects cannot be neglected. It is found that the motion consists of modulated damped oscillations, with the damping parameter and frequency approaching only asymptotically the results of the normal-mode analysis. The connexion with the normal-mode method is demonstrated explicitly and the experimental relevance of our results is discussed.

An experimental examination of the fundamental properties of free turbulent interactions in a mixing flow has been conducted. A turbulent, two-dimensional, incompressible, uniform-density mixing layer was produced by using a parallel bar grid of different bar spacings but the same space to bar diameter ratio M/D = 2. In this unique mixing-flow geometry, two initially parallel flowing streams of air were formed in such a way as to possess the same mean structure but different turbulent kinetic energy. The mixing phenomenon was driven solely by the turbulent kinetic-energy self-diffusion process.

The data showed the development of the turbulent properties without the interference caused by turbulence generated by a mean shear flow. A simple diffusion model was constructed by assuming an analogy between the unsteady gradient diffusion process and the transport of turbulent kinetic energy by the fluctuations. An empirical error function least squares curve fit, a diffusional power law and diffusion coefficients were derived. The empirical coefficients of self-diffusion were found to be 10.4 and 68.6 cm2 s−1 for the longitudinal and transverse turbulent energy components, or about a hundred and five hundred times faster than molecular viscous shear diffusion, respectively. This self-diffusion mechanism by microscale size eddies may account for some of the error found by other investigators in balancing the measured terms of the turbulent kinetic-energy equation.

In our previous qualitative paper, it was shown that when a vertical ice surface melts into a stable salinity gradient, the melt water spreads out into the interior in a series of nearly horizontal layers. The experiments reported here are aimed at quantifying this effect, which could be of some importance in the application to melting icebergs. Experiments have also been carried out with heated and cooled vertical walls at larger Rayleigh numbers R than those of previous experiments.

The main result is that for most of our experiments there is no significant difference between these three cases when properly scaled. The layer thickness over a wide range of R is described to within the experimental accuracy by \[ h=0.65 [\rho(T_w,S_{\infty}) - \rho(T_{\infty},S_{\infty})]\left/\frac{d\rho}{dz}\right., \] where the term in brackets is the horizontal buoyancy difference evaluated at the mean salinity and dp/dz is the vertical density gradient due to salinity. In the case of ice melting into warm water the effective wall temperature Tw is approximately 0°C, whereas in colder water the freezing point depression must be taken explicitly into account. A detailed examination of the vertically flowing inner melt water layer in both homogeneous and salinity stratified cases has been made. This layer and the melt water which is mixed outwards from it into the turbulent horizontal layers have little effect on the outer flow. At high R and large external salinity, however, mixing can reduce the effective salinity at the inner edge of the horizontal layers, and thus the layer scale. A puzzling feature is the relatively weak dependence of layer scale on local salinity, though the vigour of convection and the rate of melting are greater where the salinity is high.

The direct application of our results to oceanographic situations predicts layer scales under typical summer conditions of order tens of metres in the Antarctic and of order metres in the Arctic. More measurements will be needed, especially close to icebergs, before the application of these ideas to polar regions can be properly evaluated.

In natural convection in a porous medium heated from below, the convective flow in two dimensions becomes unsteady above a certain critical Rayleigh number and exhibits a fluctuating or oscillatory behaviour (depending on the confinement in the horizontal dimension). This fluctuating behaviour is due to a combination of the instability of the thermal boundary layers at horizontal boundaries together with a ‘triggering’ effect of earlier disturbances. The point of the origin of the instability of the thermal boundary layer appears to play a dominant role in determining the regularity of the fluctuating flow. This numerical study investigates the importance of this point of evolution and concludes that there may exist more than one oscillatory mode of convection, depending on its position. The investigation focuses on the symmetry of the flow and demonstrates that with stable and accurate numerical schemes, an artificial symmetry may be imposed in the absence of realistic physical noise. If an initially symmetric perturbation is imposed the flow retains an essentially symmetric flow pattern with a high degree of regularity in the oscillatory behaviour. The imposition of an asymmetric perturbation results in a degradation of regularity. The appearance of the symmetric, regularly oscillatory flow is characterized by a symmetric (and stationary) arrangement of the points of origin of the instability of the upper and lower thermal boundary layers; in the case of the irregular oscillations the points of origin are not symmetric and their locations are not fixed.

The response of the near field of a free, plane air jet (aspect ratio 44:1) to a controlled, sinusoidal perturbation was investigated by hot-wire measurements. The experiments were carried out at an exit excitation amplitude of 1·4 % for the Strouhal number range 0·15 [les ] StH [les ] 0·6 and the Reynolds-number range 8 × 103 [les ] ReH [les ] 3·1 × 104. The influence of the excitation, introduced with a loudspeaker attached to the jet settling chamber, on the mean and fluctuating velocity fields is much weaker than that in the circular jet. The amplitude and phase profiles of the fundamental, educed through phase-locked measurements, show that the induced symmetric mode remains symmetric as it travels downstream. The wave growth rate is much higher and the wavelength much smaller in the shear layer than on the centre-line of the jet. The wave fundamental attains its maximum amplitude at StH ≃ 0·18 on the jet centre-line and at StH ≃ 0·45 in the shear layer. The amplitude profiles of the fundamental in the shear layer agree quite well with the spatial stability theory of Michalke (1965b); however, the phase data do not agree well with the theoretical predictions. The growth rate and the disturbance wavenumber increase monotonically with the StH both in the shear layer and on the centre-line but tend to approach constant values at higher StH. The phase velocity data show that, in the lower Strouhal-number range, the plane jet acts as a non-dispersive waveguide.

The spectral turbulent diffusivity (STD) theory, originally deduced from a spectral generalization of the gradient-transfer theory (Berkowicz & Prahm 1979), is here derived from a basic concept of turbulent mixing for the case of homogeneous turbulence. The turbulent mixing is treated in a way similar to Prandtl's mixing-length concept. The contribution to the turbulent flux from eddies of different length is represented by a linear superposition. The spatial variation of the concentration distribution is described in terms of Fourier series. This procedure results in the spectral diffusivity formulation, which is Eulerian and scale dependent. If the concentration distribution is approximated by a truncated Taylor expansion instead of an exact representation by the Fourier series, the gradient-transfer approximation is retrieved.

The turbulent energy density, as function of the eddy length, is related to the eddy transport velocity and a probability of the occurrence of the eddies. The eddy transport velocity, derived from the relation between the energy spectrum and the Lagrangian correlation function, is used for computation of the spectral turbulent diffusivity. The turbulent energy spectrum is approximated by the inertial sub-range form $(-\frac{5}{3}$ law). The STD coefficient obtained here has, for large wavenumbers, a slope of $k^{-\frac{4}{3}}$ as predicted previously.