The method of matched asymptotic expansions is employed for investigating the effect of a uniform current on the velocity field of a viscous, incompressible, conducting fluid streaming past a stationary conducting ellipsoid of revolution, assuming that the Reynolds number is small. It is also assumed that at infinity the velocity and uniform current are parallel to the axis of the ellipsoid. It is found that the presence of the current increases or decreases the drag coefficient, depending on whether the fluid conductivity is larger than that of the ellipsoid or vice versa. It is suggested that this effect of the current on the drag coefficient holds for all axisymmetric bodies that are also symmetric about a plane perpendicular to their axis. The case of a circular disk broadside on the undisturbed current, obtained as a special case of a planetary ellipsoid, is slightly different; when the conductivity of the disk is non-zero the electromagnetically induced flow field vanishes.

The cross-correlation technique has been used to obtain statistical properties of scalar density fluctuations. Two schlieren instruments with their optical beams intersecting in the turbulent field each give a signal proportional to the density gradient in the flow direction but integrated along the beam path. Cross-correlation of the two signals gives an area integral of the density-gradient covariance. For locally isotropic conditions the area integration can exactly compensate for the two gradients giving a result proportional to the local mean-square density fluctuation at the beam intersection point.

Experiments performed in the shear layer of a subsonic jet show results which tend to verify the principles of crossed-schlieren measurement. Intensity levels are close to those predicted assuming density fluctuations are related isentropically to local, incompressible pressure fluctuations.

Cheng's analysis of strong viscous interaction between a laminar boundary layer growing over a flat plate and the external hypersonic flow field is extended to cover curved surfaces. It is demonstrated that the solutions for some concave surfaces are oscillatory and quantitatively unrealistic. The reason for this behaviour is that the Busemann term in the Newton–Busemann pressure law used in Cheng's analysis over-corrects for centrifugal effects. The removal of the Busemann term or the substitution of the tangent-wedge pressure law results in an alternative analysis which can cover both strong and weak viscous interaction over a wide variety of two-dimensional shapes. A number of examples are included together with comparative experimental data.

The acoustic scattering properties of a semi-infinite compliant plate immersed in turbulent flow are considered in the context of Lighthill's theory of aerodynamic noise. The turbulent eddies are replaced by a volume distribution of quadrupoles, and the reciprocal theorem used to transform the quadrupole scattering problem into one of the diffraction of a plane acoustic wave. This problem is solved by the Wiener–Hopf technique for the case when elastic forces in the plate are negligible, so that a local impedance condition relates the plate velocity to the pressure difference across the plate. Strong scattering of the near-field into propagating sound occurs when certain types of quadrupole lie sufficiently close to the plate edge, and we derive explicit expressions for the scattered fields in various cases. When fluid loading effects are small, and the plate relatively rigid, the results of Ffowcs Williams & Hall (1970) are recovered, in particular the U5 law for radiated intensity. A quite different behaviour is found in the case of high fluid loading, when the plate appears to be relatively limp. The radiated intensity then increases with flow velocity U according to a U6 law. In aeronautical situations, surface compliance is negligible in its effect on the scattering process, and the U5 law must then apply provided the surface is sufficiently large. On the other hand, the effect of appreciable surface compliance is to greatly inhibit the near-field scattering from the surface edge. This weaker scattering is likely to be observed in underwater applications, where fluid loading effects are generally so high as to render unattainable the condition for a plate to be effectively rigid.

An analytic solution of the non-isentropic equations of gas-dynamics, for the one-dimensional motion of a non-viscous and non-conductive medium, is derived in this paper for the first time. This is a particular solution which contains only one arbitrary function. On the basis of this solution, the interaction of a centred simple wave with a shock of moderate strength is analyzed; and it is shown that, for a weak shock, this analysis is compatible with Friedrichs's theory. Furthermore, in the light of this analysis, it is explained why the empirical methods employed by the shock-expansion theory, including Whitham's rule for determining the shock path, work.

The effect of a density stratification on the steady, mechanically driven motion of a viscous fluid in a rotating cylinder with axis aligned with the rotation and gravity vectors and with parallel top and bottom surfaces that slope with respect to the plane perpendicular to the rotation vector is studied by a linear theory. Primary attention is given to a study of the alteration of the characteristics of the flow of a homogeneous fluid by the addition of a weak stratification. It is found, for example, that in the range $E^{\frac{3}{2}} < \sigma S < E$, where E = ν/ΩL2 and σS = ναgΔT0/κΩ2L, and with a homogeneous boundary condition on the perturbation temperature, the interior velocity is parallel to the direction perpendicular to the plane determined by the vector normal to the top surface and the rotation vector. The circulation closes in an inviscid, but heat-conducting, boundary layer of thickness E¾(σS)−½ on the side wall. Thus, with stratification, the steady flow in this configuration differs markedly from the corresponding flow in a cylinder where the top and bottom surfaces lie in planes perpendicular to the rotation vector. The difference is caused by the fact that in the container with sloping surfaces the basic stratification interacts with the geostrophic flow whereas, in the other case, the interaction is with the much smaller Ekman layer suction velocities.

A general theory is presented which describes disturbances generated by large amplitude, high frequency pulses in stratified media. The theory is used to discuss large amplitude, but shockless, acoustic pulses propagating under the influence of a constant gravity force into an atmosphere which need not be in thermal equilibrium before their arrival.

The modulating influences of pressure and temperature stratification on the amplitudes of such pulses as they move towards or away from earth are described in detail.

The paper generalizes techniques already established by Whitham (1956) so that they are applicable to disturbances of any amplitude.

The break-up mechanism of axisymmetric liquid sheets formed by the impingement of two co-axial jets has been examined. Three break-up regimes in the Weber number range from 100 to 3 × 104 are reported. In the first break-up regime, droplets are formed through successive mergings of liquid beads along the nearly circular periphery of the sheet. The formation of beads is caused by Rayleigh instability. In the transition regime, Taylor's cardioid wave pattern prevails in the first half of this regime, while the sheet begins to flap in the second half.

In the second break-up regime, antisymmetric waves on the sheet grow radially. A semi-empirical equation has been deduced to predict the break-up radius of the sheet. The motion of an axisymmetric vibrating membrane with radially decreasing thickness has been studied to include Helmholtz instability as an analogue of the wave motion of the expanding circular sheet. A distorted progressive wave equation has been solved by the WKBJ method to indicate the effect of cylindrical geometry. The calculated wave speed agrees fairly well with experimental data at low Weber numbers.

Taylor (1953, 1954a) showed that, when a cloud of solute is injected into a pipe through which a solvent is flowing, it spreads out, so that the distribution of concentration C is eventually a Gaussian function of distance along the pipe axis. This paper is concerned with the approach to this final form. An asymptotic series is derived for the distribution of concentration based on the assumption that the diffusion of solute obeys Fick's law. The first term is the Gaussian function, and succeeding terms describe the asymmetries and other deviations from normality observed in practice. The theory is applied to Poiseuille flow in a pipe of radius a and it is concluded that three terms of the series describe C satisfactorily if Dt/a2 > 0·2 (where D is the coefficient of molecular diffusion), and that the initial distribution of C has little effect on the approach to normality in most cases of practical importance. The predictions of the theory are compared with numerical work by Sayre (1968) for a simple model of turbulent open channel flow and show excellent agreement. The final section of the paper presents a second series derived from the first which involves only quantities which can be determined directly by integration from the observed values of C without knowledge of the velocity distribution or diffusivity. The latter series can be derived independently of the rest of the paper provided the cumulants of C tend to zero fast enough as t → ∞, and it is suggested, therefore, that the latter series may be valid in flows for which Fick's law does not hold.

Similarity rules are constructed for the load distributions induced on a thin two-dimensional wing at subsonic speeds by sinusoidal gusts whose wave fronts are at an angle to the leading edge of the wing. It is shown that these rules divide into two groups according to the value of a parameter dependent on the Mach number and the angle between the gust front and the wing. The similarity rules for each group relate all the members of the group to a simpler problem whose solution can be found by existing methods. The similarity between the two groups is also discussed in terms of the two methods of solution available and it is shown that each method of solution is applicable in all cases.

The astrophysical importance of the hypothesis that vorticity is expelled from regions of strong turbulence is briefly reviewed. An experiment from which Gough & Lynden-Bell claimed to provide positive evidence of vorticity expulsion has been repeated. The results are reproduced here and are shown to be due to thermally driven circulation currents. No unambiguous laboratory evidence for (or against) the vorticity expulsion hypothesis therefore exists at present.

The stability of the laminar flow in a rectangular channel with aspect ratio 1:8 was investigated experimentally, with and without artificial excitation. The critical Reynolds number based on the hydraulic diameter and the average velocity was found to be 2600. Behaviour of damped and growing waves, using artificial excitation, was examined in detail. In particular the progress of growing disturbances was followed. Breaking was found to be the ultimate fate of a growing wave. Spectra of growing and damped waves were also obtained. Measurements were made for wavelengths, wave speeds and amplification or damping rates. The neutral stability boundary in the αr, R plane was determined. In the damped region, comparison of several aspects of the behaviour of the measured disturbances with the plane Poiseuille theory for spatial decay yielded good agreement.

Three-dimensionality and non-linear subcritical instability were briefly examined. Neutral subcritical waves at low Reynolds numbers appeared possible when the exciter amplitude was quadrupled.

The possible bearings of the present study on the stability of plane Poiseuille flow are suggested.

This paper discusses the linear theory of the transmission of an acoustic pulse through a plane discontinuity of velocity. It is shown that elementary ideas of geometrical acoustics which have received much attention in the recent literature lead to the erroneous prediction of a zone of silence. It is in precisely this zone that unstable disturbances and broad-fronted pulses of enhanced intensity propagate, having been triggered-off by the arrival of the pulse at the vortex sheet. The apparent qualitative agreement between geometrical acoustics and experimental data regarding sound radiation from the interior of supersonic jets is shown to be purely fortuitous, and it is argued that a complete analysis of such problems must depend on a deeper and possibly non-linear treatment.

The wave drag coefficient is computed approximately for a nozzle containing a swirling flow as a function of R0−1, the inverse of the Rossby number. When R0−1 < λ1 and R0−1 = λn, where λn denotes the nth zero of the Bessel function J1, there is no wave in the flow and the wave drag is zero. The drag coefficient is found to be sub-divided into different regions between R0−1 = λn and λn+1, with n = 1,2,3,.… When each λn is exceeded, the drag coefficient jumps from zero to a value which is one order higher than its values in the previous region (except in the case n = 1), and then decreases to zero as R0−1 increases toward λn+1. Very high wave drag can be expected in flows of large swirl ratios.

We discuss the diffraction of internal waves by a semi-infinite vertical barrier in a uniformly rotating, stably stratified fluid of constant depth and Brunt–Väisälä frequency. N, For the frequency passband f < σ < N, where f and σ are respectively the inertial and wave frequencies, the presence of rotation gives rise to internal Kelvin waves which propagate without attenuation along the barrier. For the passband N < σ < f, however, the barrier generates waves which propagate without attenuation away from the barrier and which have amplitudes that fall off exponentially in the direction along the barrier.

Energy and linear limits are calculated for the Poiseuille–Couette spiral motion between concentric cylinders which rotate rigidly and rotate and slide relative to one another. The addition of solid rotation can bring the linear limit down to the energy limit with coincidence achieved in the limit of infinitely fast rotation. If the differential rotation is also added, the solid rotation rate need be only finite to achieve near coincidence. Sufficient conditions for non-existence of sub-linear instability are derived. The basic spiral character of the instability is analysed and the results compared with the experiments of Ludwieg (1964).

Using a simplified wave-diagram and the gas-speed/sound-speed diagram, it is shown how the oscillations start and grow within a resonance tube. It is found that the oscillation amplitude tends to a limiting value which is obtained when the jet is fully swallowed by the tube during the phase of compression of the cycle. Experiments are carried out for jet Mach numbers from 0·1 up to 2. To achieve an adequate evacuation of the tube in the expansion phase, a thin cylindrical body must be used, which is laid along the axis of the jet to produce a wake and a correlative local deficiency of the kinetic energy of the jet. Measured amplitudes of pressure fluctuations are in good agreement with theoretical values.

Oscillatory flow in a turbulent boundary layer is modelled by using a coefficient of eddy viscosity whose value depends upon distance from a fixed boundary. A general oscillatory flow is prescribed beyond the layer, and the model is used to calculate the mass transport velocity induced by this within the layer. The result is investigated numerically for a representative distribution of eddy viscosity and the conclusions interpreted in terms of the mass transport induced by progressive and standing waves. For progressive waves, the limiting value of the mass transport velocity at the outer edge of the layer is the same as for laminar flow. For standing waves, the limiting value is reduced relative to its laminar value but, within the lowermost 25% of the layer, there is a drift which is reversed relative to the limiting value. This is considerably stronger than its counterpart in the laminar case and, in view of the greater thickness of the turbulent layer, it may make a dominant contribution to the net movement of loose bed material by a standing wave system.

The performance of an electromagnetic flowmeter head is assessed in terms of a weight vector W such that the output voltage ∝ ∫ v. Wdτ, where v is the velocity and τ the flowmeter volume. The condition curl W = 0 with W → 0 at ∞ is shown to be necessary and sufficient for the velocity to depend only on the flow rate and not on the flow pattern. A class of such ‘ideal’ meters is described. It is shown that meters with point electrodes can never be ideal but may, with considerable complication of the magnetic field, be made immune to asymmetric velocity-profile variations if the flow is rectilinear.

Measurements are given of the total pressure and yaw relative to the pipe axis of flow in various pipe bends attached to the end of a long straight pipe, for a pipe Reynolds number of 2·36 × 105. The behaviour of the induced secondary flows is presented in detail. In a 180° bend it is found that, from the start of the bend, the secondary flows increase to a maximum and then decrease to a steady value. This effect is explained by relating the local total pressure gradient to the production of streamwise vorticity. The same flow mechanism is used to predict qualitatively the flow pattern in an S-bend in which it is found that the secondary flows cause a complete interchange of the slow moving wall fluid and the faster central core. Results of a computer program for calculating the secondary flow from a knowledge of the upstream velocity profile are included. Although real fluid effects, other than those causing the upstream velocity profile, are omitted from the computations, the measured flow pattern is reasonably well predicted in a long bend up to a bend angle of about 75°.