Recently Cheng & Akiyama (1970) published a numerical analysis of laminar flow in curved channels of square and rectangular section. Experimental results are presented here for flow in curved channels of square section. The channels were toroidal in shape, and the flow was driven electromagnetically. Various ratios of the channel dimension d to the channel radius of curvature, R, were used to investigate the dependence of friction factor, f, on the Dean number K, and the Reynolds number, Re. For 5 × 102 < K < 7 × 104 the formula (fRe) = 1·51 K½ was found to fit all the results, although R/d was varied from 17·5 down to the low value of 1·75. At lower values of K the analysis of Cheng & Akiyama was approximately validated.

The theory of Hunt & Stewartson (1965) for MHD flow in a rectangular duct with conducting walls parallel and non-conducting walls perpendicular to the magnetic field is applied to the problem of electrically driven MHD flow in a rectangular annulus. It is assumed that the Hartmann number M is sufficiently great for secondary flow effects to be negligible. The experiment described here satisfied the conditions of the theory and thus provides a sensitive experimental check on Hunt & Stewartson's theory. The theory is found to agree with the experiments to within the accuracy of the asymptotic theory.

The paper presents an approximate analysis for high Hartmann number of the flow of an electrically conducting, incompressible fluid in a duct of square crosssection, having one pair of opposite walls insulating, and the other pair perfectly conducting and inclined at arbitrary orientation to a uniform transverse magnetic field. The flow is considered to be either pressure-driven with the two perfectly conducting electrodes short-circuited together or electrically driven by a potential difference applied between these electrodes in the absence of axial pressure gradient. The paper describes experiments on the pressure-driven, short circuited case using mercury in copper ducts to investigate the variation of the streamwise pressure gradient and of the potential distribution along one insulating wall with orientation, magnetic field and flow rate.

At general orientations the analysis suggests and the experiments confirm the existence of regions of stationary fluid in the corners of the duct, together with viscous shear layers parallel to the magnetic field. For the case in which the electrodes are parallel to the magnetic field the experimental results for the pressure gradient, but not those for the potential distribution, agree reasonably well with Hunt & Stewartson's (1965) asymptotic solution. Both pressure gradient and potential results agree closely with the analysis by Hunt (1965) of the case in which the electrodes are perpendicular to the magnetic field.

The method of multiple scales is used to analyze three non-linear physical systems which support dispersive waves. These systems are (i) waves on the interface between a liquid layer and a subsonic gas flowing parallel to the undisturbed interface, (ii) waves on the surface of a circular jet of liquid, and (iii) waves in a hot electron plasma. It is found that the partial differential equations that govern the temporal and spatial variations of the wave-numbers, amplitudes, and phases have the same form for all of these systems. The results show that the non-linear motion affects only the phase. For the constant wave-number case, the general solution for the amplitude and the phase can be obtained.

Measurements of turbulence energy diffusion and the spectral distributions of stress components in the core of turbulent pipe flow are presented. The results tend to confirm the proposal of Bradshaw (1967a, b) that an inertial subrange in the spectra can exist at quite modest laboratory Reynolds numbers. They also illuminate the inconsistencies in Laufer's (1954) measurements of dissipation and suggest that the fitting of a −5/3 power law to the spectra may well provide the most accurate method of determining dissipation for Re [gsim ] 105.

A von Kármán vortex street generated in the usual way was subjected to a deceleration, thereby changing the ratio of longitudinal to lateral spacing between the vortices. Distortion of the individual vortices followed which resulted in annihilation of concentrated vortex regions and creation of a stationary wake flow. This wake flow was itself dynamically unstable and developed into a new vortex street of a different frequency from the initial one. The breakdown of the initial vortex street is qualitatively explained by considering the convection of a concentrated vortex region due to the motion imposed by all the other vortices.

The initial-value problem for linearized perturbations is discussed, and the asymptotic solution for large time is given. For values of the Reynolds number slightly greater than the critical value, above which perturbations may grow, the asymptotic solution is used as a guide in the choice of appropriate length and time scales for slow variations in the amplitude A of a non-linear two-dimensional perturbation wave. It is found that suitable time and space variables are εt and ε½(x+a1rt), where t is the time, x the distance in the direction of flow, ε the growth rate of linearized theory and (−a1r) the group velocity. By the method of multiple scales, A is found to satisfy a non-linear parabolic differential equation, a generalization of the time-dependent equation of earlier work. Initial conditions are given by the asymptotic solution of linearized theory.

Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.

To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

A symposium on aerodynamic noise was held at Loughborough University from 14 to 17 September 1970 under the sponsorship of the Royal Aeronautical Society and the British Acoustical Society. The objective of the meeting was to focus attention on unsolved theoretical and experimental problems which will require attention over the next few years. Areas which were covered included jet noise, nonlinear acoustics, rotor noise, and diffraction theory. The symposium was successful in bringing together several new themes in aerodynamic noise research. The most significant of these were the existence of a degree of order in turbulent jet flows, and the dominant effect of inflow conditions on rotor noise radiation. In addition an improved and unified basis for jet noise theory seems to be evolving.

Centrifugally driven circulations in a rapidly rotating cylinder of fluid heated differentially in the vertical are considered. Boundary-layer solutions obtained previously are extended to include large diameter/height aspect ratios and a centrifugal acceleration of the same magnitude as that of gravity. The ratio of convective to conductive heat transfer is small in the region of parameter space considered. The effect of the circulations on the asymptotic stability of a fluid heat from below and subjected to Coriolis force is then considered. Away from the side wall of the cylinder the basic state circulation increases the critical Rayleigh number at which gravitational instabilities occur; however, a destabilization near the side wall is possible.