The turbulent flow of a weakly conducting liquid between parallel plates in the presence of a transverse magnetic field is investigated. The form of the mean velocity profile is determined by a series of constraints resulting from the boundary conditions and the Navier–Stokes equations and by the Malkus postulates on the spectrum of the mean vorticity gradient. The width of the transition regions near the walls is derived in terms of the governing dimensionless numbers and this expression is checked, in the asymptotic laminar case, against the well-known Hartmann result. A graphical method, exploiting the relation between the boundary region thickness and the smallest scale of motion defined by the Malkus theory is proposed to determine the scale of the velocity profile, i.e. the flow rate in terms of the pressure gradient and the magnetic field strength.

A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method.

In a recent study related to transition in the wake flows behind circular cylinders held transversely to an air stream, Bloor (1964) has reported the observation of velocity ‘spikes’ and attributed these to the close proximity to the hot wire of vortex centres on the opposite side of the von Kármán vortex street. Further observations of spikes are reported here, and the characteristics of their distribution indicate that other explanations of their form must be found. Some idealized flows are considered, and it is concluded that observations of spikiness within the hot-wire output may be accountable in terms of large-scale distributions of vorticity within the flow convected past the wire, the distributions being reasonable representations of a separated flow. The observations also provide some evidence that small vortices of Strouhal frequency exist on the inside of the coherent separated shear layer, and this may assist in the understanding of the feed-back mechanism where by the von Kármán street establishes itself as a self-perpetuating phenomenon.

The hypersonic strong-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier–Stokes equations as a basis. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number σ, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number M, the free-stream Reynolds number based on the plate length RL, and the interaction parameter x = {(γM2)2+ω/RL}½, go to infinity.

Through the use of asymptotic expansions and matching, it is shown that, for (1−ω) > 0, three distinct layers for which similarity exists make up the region between the shock wave and the plate. The behaviour of the flow in these three layers is analysed.

The investigation to be described here is a wide-ranging experimental study aimed at determining both the details of the flow field and the pressure drop and friction factor characteristics for turbulent flow in eccentric annular ducts. The experiments were performed utilizing three annular ducts of different diameter ratios; in each case the eccentricity was varied from zero (concentric annulus) to unity (walls in contact). To provide the broadest possible perspective, the measurements of the velocity field are presented in three different ways. First, contour maps showing lines of constant velocity are constructed. From these are deduced circumferential distributions of the local shear stress on the bounding walls. Velocity profiles along lines normal to the walls are represented in terms of both law-of-the-wall variables and defect-law variables. Neither of these representations affords complete agreement with the universal circular-tube distributions. In general, the defect law provides a somewhat closer correlation of the results for the eccentric annulus with those for the tube. The experimental findings do not substantiate a prior analytical model which assumes that the universal law of the wall applies on all lines normal to the bounding walls of the annulus. Friction factors, based on static pressure measurements, are shown to decrease with increasing eccentricity. The measured friction factors are in fair agreement with those of analysis. Hydrodynamic development lengths, deduced from entrance-region pressure data, are found to increase with increasing eccentricity. Circumferential pressure variations also increase with eccentricity.

The development of the boundary layer accompanying the formation of a free surface at y′ = 0, from the two-dimensional uniform shear flow u′ = ωyω, is discussed. The analysis shows that the surface velocity and surface position vary as the cube root of the distance downstream, while the mass-transfer coefficient varies inversely as the cube root of this distance. It is shown how these may be applied to the formation of capillary jets.

An approximately homogeneous turbulent shear flow is generated in an open-return wind tunnel test-section by a plane parallel-rod grid of uniform rod diameter and non-uniform rod spacing. The grid design is based upon an analysis by Owen & Zienkiewicz (1957). Hot-wire measurements taken in this flow include mean velocities, component turbulence intensities, shear and two-point space correlations, and energy spectra. In addition, microscales, obtained both from instantaneous time derivatives of the hot-wire signal and from two-point space correlations, and integral scales, calculated both from correlations and energy spectra, are reported.

Based upon these results, it is concluded that, far enough away from the grid and the test-section wall boundary layers:

1. The turbulence intensities are maintained at uniform values by the nearly constant mean shear.

2. The turbulent shear stress approaches an asymptotic value.

3. Measured two-point space correlation coefficients and one-dimensional energy spectra attain self-preserving forms.

4. When distance downstream of the grid is measured in terms of the number of ‘local’ grid rod spacings, (see discussion of microscales obtained from time derivatives), the Taylor microscale defined by the correlation coefficient Ruu(rX, 0, 0) grows linearly with this ‘effective’ distance over most of the region measured.

5. The limited number of integral scale determinations and experimental uncertainty allow only the statements that the magnitude of the longitudinal scale is roughly one-eighth the lateral dimension of the square test-section and tends to increase slightly with ‘effective’ distance from the grid.

6. The lateral integral scales are approximately one-half the longitudinal scales and also increases with distance from the grid.

7. The integral scale which characterizes the size of the eddy primarily responsible for momentum transfer is roughly one-tenth the test-section lateral dimension (measured at one point only).

The problem studied here is that of the attenuation of internal waves through turbulent mixing in a weakly and exponentially stratified fluid. The equations are linearized and it is assumed that the action of turbulence can be parametrically represented by eddy mixing coefficients and that the influence of bottom friction is restricted to a thin bottom boundary layer. The simple case where there is no rotation and only one component to the stratification is first examined in detail, and the modifications caused by introducing rotation and a second component are subsequently investigated. Subject quantitatively to the choice made for the eddy coefficients, but qualitatively not strongly dependent on that choice, the following conclusions are drawn: (i) very short internal waves (length < 100 m) are strongly damped in basins of all depths; (ii) long internal waves or seiches in shallow seas (depth ≃ 100 m) will not last more than a few cycles as free oscillations; (iii) the attenuation rate for long internal tides is small enough that these should be observable very far from the coasts, but large enough to exclude the possibility of oceanic standing wave systems; (iv) for very long internal waves the damping is predominantly due to the effect of bottom friction, and the attenuation rate becomes almost independent of the actual form of the stratification present in the fluid.

A critical scrutiny of the nature of the three-dimensional characteristics of the vortex wake of a circular cylinder serves to suggest lines for further investigation and furnishes some ideas on the nature of the growth and development of these non-uniformities. It is suggested that the basic occurrence in the growth of three-dimensionality is the continuation of vortex lines, oriented more or less parallel to the body, into the direction of the free stream. The causes of this vary, as do the details of the development with the particular situation considered.

Experiments were performed in a wind tunnel at Reynolds numbers based on cylinder diameter of 85, 235 and 2 × 104, at which stable, transitional and turbulent vortices were investigated.

The solution for the flow of a fully ionized gas over a wedge of finite angle is known for the case when the applied magnetic field is aligned with the incident stream. In this flow there are current sheets on the surfaces of the wedge. When the magnetic field is allowed to deviate slightly from the stream, the current sheets may move into the gas and become shock waves. The magnetic fields adjacent to the wedge above and below it have to be matched. A perturbation method is introduced by means of which expressions for the unknown quantities in the different regions may be determined when there are four shocks attached to the wedge. The results give insight into the manner in which the shock-wave pattern develops as the obliquity of the magnetic field to the stream increases. The question of the stability of the shock waves is also examined.

The assumptions of the shock-expansion method are re-examined. Although the shock-expansion method and Whitham's rule are used to treat two different classes of problems, certain similarities between these two methods are noted. It is suggested that a single procedure leads to solutions for the entire flow field for both classes of problems.

The shape of a jet of Newtonian liquid issuing from a capillary needle into air is considered. The results of two theoretical approaches are presented. One approach is a perturbation analysis about the final state of the jet and the other is a boundary-layer analysis near the point of jet formation. Comparison of the predictions with experimental jet shapes shows them to be in semi-quantitative agreement. Especially interesting is the presence of a ‘discontinuity’ in the empirical exponential decay rate of the jet radius occurring at a Reynolds number somewhere between 14 and 20 and the correspondence of this discontinuity with the peculiar behaviour in this range of the Reynolds number of the theoretical eigenvalue.

A procedure is introduced to extend the usefulness of some perturbation solutions previously presented by Libby & Fox (1963) and Fox & Libby (1964). The perturbations are now formulated about a Blasius solution with an unknown origin. This origin, an additional degree of freedom, is selected, in the spirit of local similarity, so that it will yield a better approximation to the initial profile. With this modification the basic solution will handle a much wider class of problems successfully. Numerical examples are presented to demonstrate the improved accuracy and applicability of this new scheme.