The flow of an electrically conducting fluid up a hot vertical plate in the presence of a strong magnetic field normal to the plate is considered. A solution is developed based on the idea of matching ‘outer’ and ‘inner’ solutions in the moving layer of fluid. An approximate Pohlhausen method of solution is also given which yields results in fairly good agreement with the exact analysis.

Viscous flow perpendicular to a line (or ‘grating’) of evenly spaced identical cylinders is considered in the case when the spacing between the cylinders is much smaller than their cross-sectional dimensions. Lubrication theory is used to find the pressure drop across the grating and hence the force on each cylinder. A square array (or ‘lattice’) of closely packed cylinders is similarly treated.

A general reverse-flow relation is obtained within the framework of second-order (in surface deflexion) supersonic flow theory. From this it is shown that the second-order increment in the drag of an arbitrary quasi-cylindrical body can be expressed as surface and volume integrals of the first-order solutions corresponding to forward and reverse flow past the body. Analogous results are obtained for second-order transverse forces and moments on an arbitrary quasi-planar wing, where the first-order reverse flow must correspond to certain zero-thickness wings. Other similar results are possible. Thus, second-order aerodynamic forces on bodies may be obtained from first-order solutions by quadrature. It is also shown that the reverse-flow integral relation can yield the pressure distribution on the surface by inversion of an integral equation constructed therefrom. It is thought that these results should be particularly useful for the Machnumber range between that of linearized theory and that of full hypersonic small-disturbance theory.

The flow field due to the oscillations of a disk is governed largely by diffusion near the boundary, but the inertia forces cannot be neglected at large distances. The solution is obtained as a single expansion for the case when the disk is performing small-amplitude sinusoidal oscillations.

The problem of flow of an inviscid, incompressible fluid inside a circular pipe, with a sphere on the axis of the pipe, has been studied by Lamb (1936) (irrotational flow), Long (1953) and Fraenkel (1956) (swirling flow). Because of the difficulty of satisfying all the boundary conditions in the problem, only approximate solutions, valid for spheres of small diameter (compared with that of the pipe) have been obtained. In this paper, it is found that by introducing a vortex sheet over a segment of the diameter of the sphere, flow patterns can be obtained by an inverse method for the case of large spheres. Four different types of flow are considered: (1) irrotational flow, (2) swirling flow with constant axial and angular velocities far upstream, without lee waves, (3) swirling flow with constant axial and angular velocities far upstream, with lee waves, and (4) rotational flow with a paraboloidal velocity distribution far upstream.

The properties of a turbulent flow are often described in terms of velocity correlations in space, in time, and in space-time. In this paper the interpretation of velocity correlation measurements which are made in a region of highintensity turbulence is considered in some detail. Under these conditions it is shown that some account must be taken of the effects of both mean and fluctuating shear stresses which are continuously modifying the turbulent structure. For an almost frozen pattern, for example, in the turbulence behind a grid, the turbulent convection velocity is amost equal to the mean flow velocity, while the space correlation and auto-correlation of the velocity fluctuations are simply related through this velocity. In contrast to this, when the intensity is high, the convection velocity may differ considerably from the mean velocity, while it is shown that different turbulent spectral components appear to travel at different speeds. This means that the turbulent spectrum and the turbulent space scales are no longer simply related. For example, the high-frequency spectral components may be ascribed to both the high-velocity eddies and the small wave-number components acting together.

Experimental results are presented which indicate the conditions under which the assumption of a frozen pattern leads to uncertainties in the subsequent interpretation of the measurements. The measurements also show that the observed difference between the mean and the convection velocity may be qualitatively explained in terms of the skewness of the velocity signals.

The problem of supersonic flow over an inclined flat-plate delta wing with supersonic edges is solved to second order in incidence. This solution for surface pressure is uniform and fully analytic. The approach utilizes a reverse-flow integral method previously developed for second-order problems. This method is augmented by a number of techniques appropriate to its framework. The simplification over standard techniques achieved by using these reverse-flow methods is quite substantial and makes the problem tractable.

Reverse-flow procedures give a volume-surface integral relation that connects the second-order forward flow over the body of interest with the linearized reverse-flow over a related body. A singular integral equation is generated from the integral relation by introducing the edge sweep of the reverse-flow wing as a free parameter. An inversion is available which gives the second-order solution on the surface of the wing. The solution is then made uniformly valid using techniques previously developed.

A study has been made of the factors influencing the break-down of sheets formed by the impingement of two liquid jets. It is shown that disintegration generally results from the formation of unstable waves of aerodynamic or hydrodynamic origin. While the characteristics of the former waves are fairly well understood, little is known about the latter. The results of this study indicate that hydrodynamic (or ‘impact’) waves are generated when the Weber number of each jet (ρlDV2 sin 2θ/γ, where ρl is the liquid density, D the jet diameter, V the mean jet velocity, θ the half-angle of impingement, and γ is the surface tension) is above a critical value, and that their formation is independent of the Reynolds number. Drop sizes have been measured and are shown to be critically dependent upon the mechanism of disintegration.

The order of the dispersion relation for the propagation of hydromagnetic waves along a magnetized cylindrical plasma falls by unity when the plasma resistivity, σ−1, tends to zero. A consequence of this is that the two boundary conditions necessary on an insulating wall are reduced to a single condition, a reduction brought about by the development of a current sheet. If the ratio, $\Omega \equiv \omega|\omega_{ci}$ of the wave frequency to the ion cyclotron frequency is also assumed to be vanishingly small, then the nature of the single boundary condition to be adopted in the limit σ−1 → 0 depends, for the slow hydromagnetic wave, on the limiting value of ρ½Ω2 . Similarly, if Ω [Gt ] 1, and the fast hydromagnetic wave is being considered, then the relevant boundary condition is found to depend on the limiting value of Ωσ−½.

The ‘resistive’ waves that are found to accompany the fast and slow waves, in order to satisfy the boundary conditions for small but finite values of σ−1, are studied in some detail and their contribution to the wave damping is determined.

An exact solution is given for the flow in a convergent or divergent channel of a class of anisotropic fluids in which the fluid has a preferred direction.

The steady distribution function for homogeneous turbulence is studied starting from Liouville's equation, modified by the introduction of an instantaneously fluctuating external force, which acts as a random source of energy. A new technique for solving Liouville's equation is presented giving a systematic development of the concepts of turbulent diffusion and turbulent viscosity. It amounts to a consistent generalization of the random phase approximation. When the rate of input of energy into the kth Fourier component uk has a power form h|k|−α, the functional form of the mean value 〈 uku−k 〉 can be determined exactly in the limit of large Reynolds number; it is $Ah^{\frac{2}{3}}|\bf K|^ {-{\frac {1}{3}}(5+2 \alpha)}$. Liouville's equation proves an inadequate basis for the steady time-dependent mean $\langle u_k(t)u_{-k}(t^ \prime) \rangle $ and a more general equation is derived. The new equation can be solved in a similar way and shows that the time-dependent correlation starts like a Gaussian in time, then passes through an exponentially decaying state, then eventually has a power dependence $|t-t^\prime|- \gamma^ {|k|}$.

The theoretical treatments given by earlier authors are classified, reviewed and where necessary extended; then the predictions of twenty of these theories are evaluated and compared with all available experimental data, the root-meansquare error being computed for each theory. The theory of van Driest-II gives the lowest root-mean-square error (11.0%).

A new calculation procedure is developed from the postulate that a unique relation exists between cfFc and RFR where cf is the drag coefficient, R is the Reynolds number, and Fc and FR are functions of Mach number and temperature ratio alone. The experimental data are found to be too scanty for both Fc and FR to be deduced empirically, so Fc is calculated by means of mixing-length theory and FR is found semi-empirically. Tables and charts of values of Fc and FR are presented for a wide range of MG and TS/TG. When compared with all experimental data, the predictions of the new procedure give a root-mean-square error of 9.9%.

A linearized theory is developed for the oscillations of a slender body which is floating on the free surface of an ideal fluid, in the presence of incident plane progressive waves. Green's theorem is used to represent the velocity potential and the first-order slender-body potential is developed from asymptotic approximation. The general theory is valid for arbitrary slender bodies in oblique waves, and detailed results are presented for a body of revolution.

The influence of radiation on the propagation of small disturbances is investigated by considering a signalling problem and obtaining approximate limiting solutions. It is found that, for small time, the main disturbance travels at the isentropic speed of sound. For some intermediate time, the main disturbance travels at the isothermal speed of sound. For long time, the disturbance travels at the isentropic speed of sound. The decay and diffusion of these waves are also determined.

A general treatment is given of the first-order effects of wall proximity on the increased resistance to translational motions of a rigid particle of arbitrary shape settling in the Stokes régime. The analysis generalizes a previous treatment (Brenner 1962) to the case where the principal axes of resistance of the particle may have any orientation relative to the principal axes of the bounding walls. It is shown that, to the first order in the ratio of particle-to-boundary dimensions, the increased resistance of the particle can be represented by a symmetric, second-rank tensor (dyadic) whose value is independent of particle shape and orientation.

In this paper we examine the steady, two-dimensional convective motion which occurs in a horizontal circular cylinder whose wall is non-uniformly heated. One observes several qualitatively different physical phenomena depending on the wall temperature distribution and the value of the Rayleigh number. The low-Rayleigh-number behaviour for the single convective cell heated from below is related to the classical Rayleigh stability problem. The critical Rayleigh number for the single circular cell is approximately five times the value for Rayleigh's multi-celluar configuration. The flow which exhibits a nearly parabolic velocity profile near the critical Rayleigh number, gradually changes to a rigidly-rotating-core behaviour as the Rayleigh number increases. The speed of core rotation is a function of the Prandtl number, whereas the boundary-layer thickness is primarily a function of the Rayleigh number. When the heating is from side to side, the solution shows that as the Rayleigh number increases the core motion is progressively arrested leaving a narrow circulating band of fluid adjacent to the wall. An oblique heating produces a hybrid phenomenon, a low-Rayleigh-number behaviour which is characteristic of the sideways heating case and a high-Rayleigh-number interior motion characteristic of the bottom heating case. To determine the core motion in the high-Rayleigh-number limit, Batchelor's work concerning the uniqueness of incompressible, exactly steady, closed streamline flows with small viscosity is extended to include flows with small thermal conductivity.

It is suggested that the use of prolate spheroidal co-ordinates in certain problems involving slender bodies may lead to results which not only are more likely to be uniformly valid for blunt bodies, but in many cases require less complicated analysis than results obtained by standard methods which use cylindrical co-ordinates. The method is developed for a simple problem in potential theory and is then applied also to a problem in Stokes flow, yielding a procedure for obtaining the Stokes drag on a slender body of arbitrary shape. For comparison purposes, consideration is also given to the use of both cylindrical and di-polar co-ordinates, and as a by-product of the comparison of results on cylindrical and spheroidal systems some new simple formulae involving Legendre polynomials are obtained heuristically, and then rigorously proved.

The results of measurements of far-field sound emitted from jets are reported. The narrow-band power spectral density of the sound in the far field was measured for three jet diameters, three Mach numbers, and five angular positions. The intensity distribution of mean-square pressure fluctuation in the far field in several wide frequency ranges were also measured. The similarity relations found from the experiments are reported.

The transition Reynolds number and the turbulent Reynolds number induced by a sinusoidally fluctuating free stream have been determined experimentally. The oscillating flow was produced in a closed-circuit wind tunnel by means of a rotating shutter valve which had a range of frequencies from 4 to 125 c/s corresponding to a range of the dimensionless frequency parameter, $\omega v |U^2_\infty$, of 2·29 × 10−6 to 4·49 × 10−5. The dimensionless amplitude parameter, $\Delta U|U_\infty$, could be adjusted by means of shutter blades of various widths from a value of 0.0775 to 0.667.

Flows in both the free stream and the boundary layer were monitored simultaneously by means of two transistorized constant-temperature hot-wire anemometers. The transition Reynolds number, the turbulent Reynolds number and turbulent intermittency factor, γ, were determined from the velocity-time traces recorded on a dual-channel oscilloscope.

It was found that the transition Reynolds number depends only on the amplitude of the oscillations and that the dimensionless transition length is a function only of the frequency. The time-space distribution of turbulent bursts in the transition region indicates that the location as well as duration of bursts is quite regular and closely tied to the fluctuations of free-stream velocity, confirming the analysis of Greenspan & Benney.