The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient $\overline{uv^2}/\overline{u^2}\overline{v^2} $ is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.

A composite hydrodynamic-diffusion model of the arterial wall is presented to describe the vesicular transport of relatively inert macromolecules across the inner endothelial lining of the larger arteries of humans and animals and their subsequent diffusion in the underlying tissue of the intima and media. This model is motivated by the highly specialized ultrastructure of the arterial wall observed in electron microscopic studies and the recent experimental measurements of the time-dependent uptake of labelled macromolecules in animal arteries under carefully controlled in vitro conditions. The proposed dynamic model for the vesicular transport across the endothelial cell layer considers the constrained Brownian diffusion of 700 Å vesicles subject to long-range hydrodynamic and short-range London-van der Waals force interactions with the plasmalemma membranes of the endothelial cell. Approximate solutions are developed for the motion and the steady-state vesicle density distribution near the plasmalemma and in the interior of the cell using boundary-layer-like methods. The model for the vesicular transport just described appears as a novel boundary condition in the basic diffusion model for the underlying tissue. The latter is treated as a two-phase medium comprised of an interstitial fluid continuum with a uniformly dispersed smooth muscle phase as first proposed by Hills (1968). This model for the underlying tissue assumes that the smooth muscle cells contribute insignificantly to the macromolecule diffusion across the arterial wall but act as the principal storage reservoir for the macromolecules for large diffusion times because of their large volume fraction. The dimensionless parameters that arise in the theoretical model are determined by comparing the solutions for the time-dependent total wall uptake with Fry's (1973) experimental data for canine carotid artery.

The frequencies of vortex shedding from circular cylinders forced to oscillate transversely in low-turbulence uniform and shear flows were investigated. The stream velocity in the shear flow varied linearly with spanwise distance.

In both flows the vortex shedding frequency locked on to the cylinder frequency and to submultiples of the cylinder frequency. In uniform flow the range of cylinder frequencies for locking-on was dependent on the amplitude of oscillation and Reynolds number. At the boundaries of locking-on at the cylinder frequency locked-on shedding was intermittent with unforced shedding and locking-on was accompanied by a change in wake width. At a particular cylinder frequency near mid-range it is conjectured that the wake width jumped from being greater to being less than that for the stationary cylinder. In shear flow the spanwise extent of locking-on at the cylinder frequency was explained by considering the uniform flow results and the inclination of shed vortices in shear flow. At the spanwise boundaries of this locking-on, locked-on cells were shed intermittently with unforced cells which were more stable in frequency than the corresponding cells for the stationary cylinder.

Using simple Fourier transform techniques and extensions to stationary-phase methods, the behaviour of surface gravity waves is determined near triply coalescing roots of the dispersion relation. It is shown that the amplitude of the surface wave is proportional to (∂U/∂x)−¼ at the location of the triple root. Far from the triple root it satisfies conservation of action. The internal wave is modelled simply by its surface current U.

Asymptotic orders of magnitude are also given for the case ∂U/∂x = 0 at the triple root.

Possibilities of high shoreline amplification and run-up are investigated. A shoreline amplification of magnitude 5·38 and a tsunamigenic (deep water) amplification of magnitude 5·71 are obtained from single waves without analytic or computational difficulties. It is not claimed that these are a maximum, but rather it is conjectured that arbitrarily high run-up and amplification can be obtained provided that the correct initial wave trains are chosen.

An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 104to 9·76 × 105. A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 102 to 105 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 104. Comparisons between the present experimental and numerical results under similar conditions show good agreement.

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem, i.e. given blade loading. Formulae are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

In this paper we develop a uniformly valid, second-order theory for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulae for the airfoil response functions (i.e. fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1u2/u’1u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.