This paper describes a reformulation of the Lighthill (1952) theory of aerodynamic sound. A revised approach to the subject is necessary in order to unify the various ad hoc procedures which have been developed for dealing with aerodynamic noise problems since the original appearance of Lighthill's work. First, Powell's (1961 a) concept of vortex sound is difficult to justify convincingly on the basis of Lighthill's acoustic analogy, although it is consistent with model problems which have been treated by the method of matched asymptotic expansions. Second, Candel (1972), Marble (1973) and Morfey (1973) have demonstrated the importance of entropy inhomogeneities, which generate sound when accelerated in a mean flow pressure gradient. This is arguably a more significant source of acoustic radiation in hot subsonic jets than pure jet noise. Third, the analysis of Ffowcs Williams & Howe (1975) of model problems involving the convection of an entropy ‘slug’ in an engine nozzle indicates that the whole question of excess jet noise may be intimately related to the convection of flow inhomogeneities through mean flow pressure gradients. Such problems are difficult to formulate precisely in terms of Lighthill's theory because of the presence of an extensive, non-acoustic, non-uniform mean flow. The convected-entropy source mechanism is actually absent from the alternative Phillips (1960) formulation of the aerodynamic sound problem.

In this paper the form of the acoustic propagation operator is established for a non-uniform mean flow in the absence of vortical or entropy-gradient source terms. The natural thermodynamic variable for dealing with such problems is the stagnation enthalpy. This provides a basis for a new acoustic analogy, and it is deduced that the corresponding acoustic source terms are associated solely with regions of the flow where the vorticity vector and entropy-gradient vector are non-vanishing. The theory is illustrated by detailed applications to problems which, in the appropriate limit, justify Powell's theory of vortex sound, and to the important question of noise generation during the unsteady convection of flow inhomogeneities in ducts and past rigid bodies in free space. At low Mach numbers wave propagation is described by a convected wave equation, for which powerful analytical techniques, discussed in the appendix, are available and are exploited.

Fluctuating heat sources are examined: a model problem is considered and provides a positive comparison with an alternative analysis undertaken elsewhere. The difficult question of the scattering of a plane sound wave by a cylindrical vortex filament is also discussed, the effect of dissipation at the vortex core being taken into account.

Finally an approximate aerodynamic theory of the operation of musical instruments characterized by the flute is described. This involves an investigation of the properties of a vortex shedding mechanism which is coupled in a nonlinear manner to the acoustic oscillations within the instrument. The theory furnishes results which are consistent with the playing technique of the flautist and with simple acoustic measurements undertaken by the author.

A convective instability is produced by salt water diffusing onto the surface of a fresh-water layer in a Hele Shaw cell. Although the horizontal wavelength of the initial instability is small, an increase in the horizontal wavelength of the convective flow with time and depth is observed as the resulting two-dimensional convection develops. The phenomenon of wavelength variation is confirmed numerically, but quantitative observational and theoretical comparison is limited to small Rayleigh numbers. It is shown that perturbations in the density field cause horizontal pressure gradients, which in turn cause convective elements to combine.

This paper describes a model problem where compact surface vibration radiates sound into a subsonically flowing fluid. There are two distinct acoustic effects. First, the radiation is increased by flow by an amount proportional to 5M2 and that increase is shown by a general argument to arise from an enhanced surface damping and work done by the flow to overcome drag in the ratio 2:1. Second, the acoustic source strength is affected and resonance frequencies are significantly modified by flow. The main effect is that flow induces on the surface a force proportional to the displacement which opposes the action of natural surface elasticity. A critical velocity exists beyond which the surface is unstable; the stability limit is determined. The surface motion might be regarded as an acoustic monopole, but since aerodynamic fields are determined by the rate of change of the rate of mass outflow, the frequency dependence is more that of a quadrupole. Convective amplification of the sound is also shown to be that characteristic of quadrupole sources. This result indicates that real simple fields may be more sensitive to convection than might be expected from past studies of simple inhomogeneities satisfying a convected wave equation.

Mean velocities and temperatures were measured in a turbulent plume above a line heat source at the base of a vertical adiabatic wall. Various values of the buoyancy flux and distances above the source in the weakly buoyant regime of the flow were considered. Correlating expressions for the data were determined by assuming streamwise similarity of mean flow quantities, and a fixed entrainment constant and local skin-friction coefficient. The results yielded an entrainment constant based on the average velocity of 0·095±0·005. This value of the entrainment constant is in fair agreement with earlier work on wall plumes, but is less than half the value reported for free line plumes. Local flow properties are only weakly dependent upon the value of the skin-friction coefficient, with variations of 0-0·01 causing only a 3% change in the mean velocity and weight density defect. The results suggest that the presence of a wall, as opposed to a plane of symmetry, has a strong influence on entrainment, although the specific drag characteristics of the wall are of less importance. The reduced entrainment causes higher velocities and higher values of the weight density defect in a wall plume than in a comparable free plume.

The effect of large mass injection on the following three-dimensional laminar compressible boundary-layer flows is investigated by employing the method of matched asymptotic expansions: (i) swirling flow in a laminar compressible boundary layer over an axisymmetric surface with variable cross-section and (ii) laminar compressible boundary-layer flow over a yawed infinite wing in a hypersonic flow. The resulting equations are solved numerically by combining the finite-difference technique with quasi-linearization. An increase in the swirl parameter, the yaw angle or the wall temperature is found to be capable of bringing the viscous layer nearer the surface and reducing the effects of massive blowing.

An arbitrarily-shaped, closed container completely filled with fluid is considered. It is assumed that the fluid is originally in a stably-stratified state of rest, and that at an initial instant the temperature of the container walls is impulsively changed. The ensuing unsteady laminar motion is found by solving the linearized Boussinesq equations governing buoyancy-driven flows. A ‘boundarylayer/inviscid-interior’ decomposition leads to a modified asymptotic expansion scheme of analysis. The boundary-layer concept is valid only for large values of the Rayleigh number, and, in addition, we limit the Prandtl number to order unity. It is found that the inviscid interior region heats up by means of a convection process that is driven by suction induced by the boundary layer. The inviscid, adiabatic interior responds to a special horizontal ‘average’ value of the container temperature perturbation. The boundary layer smears out, or averages, any circumferential variation in this perturbation, so that the interior, in effect, responds to an isothermal boundary in each horizontal plane. The interior temperature and vertical velocity component are expressed simply in terms of this horizontal ‘average’ container temperature. The horizontal velocity potential is governed by a Poisson equation, whose solution is developed for several specific geometries to illustrate the nature of the flow.

In order to prevent stagnation and improve water quality, the intakes of many water-supply reservoirs have the form of momentum jets directed approximately radially into the storage. An analysis which idealizes this flow as consisting of a turbulent jet issuing horizontally from a circular orifice into a large rotating basin of deep water shows that the jet path is a spiral whose length scale L depends upon the rate of rotation and the kinematic momentum of the jet. Good agreement is found with flow-visualization experiments when the basin depth h is ‘large’ (h/L [gsim ] 0·21). For small depths (h/L [lsim ] 0·024) the flow tends to be twodimensional and the jet path is found to be straight. Full-scale reservoirs are usually shallow enough that the effect of the earth's rotation on the jet path is likely to be small. However these reservoirs are not inordinately shallow and tests with distorted hydraulic models are likely to show significant effects of rotation and can be misleading to the unsuspecting.

A shock-dynamic model based on the symmetrical expansion of the critical shock is used to analyse the progressive decay of an originally planar shock wave through a large and abrupt area change. This is tested against measurements of shock strength made along the axes of area changes where the shock waves are free to expand in two or three dimensions.

The critical shock is defined as the configuration when the decaying shock wave at the axis first becomes curved. The axial shock begins to decay less than one diameter from the entrance of the area change. Differences between the experimental onset of decay and the theoretical position of the critical shock are accounted for by the non-ideal behaviour of a practical pressure transducer.

The model predicts that, when the shock wave is decaying symmetrically, there is a linear relationship between a derived function ε of the decaying shock strength and the distance from the area change. This is confirmed experimentally for all the shocks studied. The quantitative application of the results in three dimensions up to 400 mm enables accurate predictions of experimental results at 1 m for M < 2·0. Also, the model may be applied to three-dimensional results to predict accurately equivalent results in two dimensions.

The numerical values of ε are based on the equivalence of the ratio of the shock areas and the ratio of their Chisnell (1957) functions. Hence correlations between experimental results and predictions of the model are evidence that Chisnell's theory can be extended to include large and abrupt area changes.

An analysis of the response of an X-probe which takes into account the axial sensitivity k, the effect of the w component of velocity and the effective rectification by the hot wire is presented. Owing to rectification points in the measured u, v ‘phase plane’ are confined within a certain sector, thus leading to distortions in the measured joint probability density functions. Numerical computations show that high turbulence intensities lead to large errors in second-order moments measured by cross-wire probes; for instance, the error in the measured correlation (over and above that due to k) can be as high as 28% when the turbulence intensity is 35%.

Pressure and pressure-velocity space correlations are calculated, using rapid-distortion theory, for turbulence in a uniform shear flow. It is found that pressure fluctuations remain correlated over significantly greater distances than do velocity fluctuations. When these predictions are used as a model for turbulence in free turbulent shear flows, it is found that the predicted scale of the pressure fluctuations is larger than the flow width. It is proposed that pressure fluctuations remain highly correlated right across free shear flows. Predictions from the theory are then compared with various experimental situations in which reasonable qualitative agreement is to be expected, and this is found.

Euromech 60 is the third in a series of European Mechanics Colloquia dealing primarily with three-dimensional turbulent boundary layers. The Colloquium was held in Trondheim at the Technical University (NTH) from 14–16 April 1975 with forty-two participants from ten different countries, and was organized by L. N. Persen and T. K. Fanneløp. A total of 23 papers were presented, dealing with both experiments on and predictions of turbulent boundary-layer flows and related topics. Those concerned with the development of prediction methods were challenged by a set of boundary-layer flow problems defined well in advance in order to be calculated prior to the Colloquium. The results show close agreement for some calculated variables and surprisingly large discrepancies in others. A brief account of this exercise is included and it will also be the subject of a special report.