An experimental study of the structure of turbulence in a conical diffuser having a total divergence angle of 8° and an area ratio of 4: 1 with fully developed flow at entry is described. Theresearch has been done for pipe entry Reynolds numbers of 152 000 and 293000 of profiles of the mean pressure, mean velocity, turbulence intensities, correlation coefficients and the one-dimensional energy spectra, but owing to similar behaviour for these two Reynolds numbers, data are presented for a Reynolds number of 293 000.

The results show that the rate of turbulent energy production approximately reaches a maximum value at the edge of the wall layer extending to the point of maximum u1-fluctuation. It is found that, within the layer, $\overline{u^2_1}$ varies linearly with the distance from the wall and the linear range grows with distance in the downstream direction.

The turbulent kinetic energy balance indicates that the magnitude of the energy convective diffusion due to kinetic and pressure effects is comparable with that of the energy production.

The propagation of nonlinear gravity–capillary surface waves in a deep slowly varying current is investigated using the conservation equations in the eikonal approximation. Graphical comparisons are made between solutions of the wave- slope and wavenumber equations for infinitesimal waves and finite amplitude waves. Finite amplitude effects are shown to be weaker for small amplitude capillary waves than for gravity waves. The ‘wave barrier’ noted by Gargett & Hughes (1972) for infinitesimal gravity waves on a slowly varying current is seen to be removed by finite amplitude effects.

The work of Dean and that of McConalogue & Srivastava on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended through the entire range of Reynolds numbers for which the flow is laminar. The coupled nonlinear system of partial differential equations which defines the motion is solved numerically by finite differences. Computer calculations are described and physical implications are discussed.

It has been conjectured for many years that plane Couette flow is stable to infinitesimal disturbances although this has never been proved. In this paper we use a, combination of asymptotic analysis and numerical computation to examine the associated Orr-Sommerfeld differential problem in a systematic manner. We obtain new evidence that the conjecture is, in all probability, correct. In particular we find that, at a fixed large value of the Reynolds number R, as in an experiment, if a disturbance of wavenumber α has a damping rate - αci then – ci has a minimum value of order R−½ when α is of order R½. We believe that this result may be an essential prerequisite to an understanding of the stability of plane Couette flow to finite-amplitude disturbances.

Davies-Jones & Gilman (1971) reported in this Journal on a linear stability analysis and second-order initial-tendency calculation for thermal convection in a thin rotating annulus heated uniformly from below. The present work gives extensive numerical calculations for an annulus model with realistic laboratory boundary conditions which extends the previous work into the finite amplitude range. The model allows the mode with the longitudinal wavenumber predicted to occur at the onset of instability to grow to a finite amplitude and induce secondary axisymmetric differential rotation and meridional circulation through its Reynolds and thermal stresses, these circulations in turn modifying the forcing cells. No higher harmonics are allowed. The Boussinesq equations for the fundamental mode and secondary circulations are solved on a staggered finite-difference grid in the annulus cross-section, mostly following the scheme laid out by Williams (1969).

Stationary convection is studied for Taylor numbers T < 3 × 103. The profile predicted for the mean circulations in the earlier analysis, that of fast rotation in the outer half, slow rotation in the inner half of the annulus (except at very high Prandtl number), together with a four-celled meridional circulation, is confirmed. For a given Taylor number T, the differential-rotation energy peaks relative to the cell energy at a modest Prandtl number P somewhat less than unity, and its production is driven mostly by the Reynolds stresses in the cells. Meridional circulation is driven by potential-energy conversion at high P and by Reynolds stresses at low P, but retains the same form for all P with increased amplitude relative to the cells at low P. For Rayleigh numbers R a given percentage above the critical value Rc the differential-rotation energy increases like T, while the meridional circulation remains nearly constant. For given P and T differential-rotation relative energy peaks at modest R/R, while the meridional circulation continues to increase. The induced differential rotation tends to distort the cell boundaries from tilted straight lines produced by Coriolis forces into S shapes qualitatively like the profile of differential rotation itself.

One example of nonlinear overstable convection is given. The induced differential rotation has time-independent and oscillatory parts. The redistribution of momentum is carried out by periodically reversing horizontal and vertical Reynolds stresses.

Experiments on fully attached flows of aqueous solutions of Polyox WSR-301 and pure solvent (tap and distilled water) about circular cylinders were carried out in the range 5 × 104 < Re < 3 × 105 for the initial purpose of providing definitive experimental information on drag reduction with additives in external flows.

During the course of the investigation, a critically degraded polymer solution was observed to cause, at a particular Re, an unforseen instability in the separation line, similar to that first observed by Brennen (1970 in fully developed cavity flows. This instability, which most easily manifest edit self in the form of an abrupt drag-force jump (here called a drag crisis) from a high subcritical to a low supercritical value, became the central issue in the investigation. Efforts to isolate the causes of this instability led to further experiments with suspensions of nearly neutrally buoyant spherical and non-spherical particles. The measurements have shown that fibres and polymer hasten transition, spherical particles do not appreciably affect the characteristics of the flow and that neither the spherical particles nor fibres give rise to a drag crisis.

A boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge. The description of the boundary-layer flow, based upon a triple-deck structure, shows how the presence of the hump generates an interaction between the inviscid region just outside the layer and the viscous region near the hump. The pressure force dominant in the boundary layer and the connexion of the local flow with the main stream develop together and are self-perpetuating, and both remain of primary significance for a wide range of hump sizes, even for a hump buried well inside the boundary layer. By consideration of the limiting cases of very small and very large humps, a consistent account of the nature of the disturbances due to the various sizes of hump is produced. The forces and couples on the hump are also evaluated.

The diffraction of a Kelvin wave by a transverse (to a straight coastline) discontinuity in depth is considered. A Fourier-integral formulation leads to a singular integral equation that may be solved exactly; however, the integrals in this solution are intractable without further approximation. An expansion to third order in a depth-change parameter yields results that are generally adequate for tidal problems (such as that posed by the Mendocino fracture zone) but are inadequate for the double-Kelvin-wave regime. Approximations are developed for a continuous change of depth that is either small or gradual, and the diffracted Kelvin wave along the coastline is found to have an amplitude that is inversely proportional to the square root of the depth and a phase that is given by the integral of the wavenumber.