Velocity measurements in a 51 mm diameter turbulent jet are presented. The measurement programme is conducted in two parts. The first part is devoted to the validation of laser velocimeter (LV) data. This consists of comparative measurements with the LV and a hot-wire anemometer. The second part consists of a survey of the jet flow field at Mach 0·28, 0·90, and 1·37 under ambient temperature conditions. Radial and centre-line distributions of the axial and radial, mean and fluctuating velocities are obtained. The distributions indicate a decrease in the spreading rate of the mixing layer with increasing Mach number and a corresponding lengthening of the potential core. The results further indicate that these two parameters vary with the square of the jet Mach number. Radial distributions collapse when plotted in terms of ση*, where σ = 10.7/(1 - 0.273 MJ2) and η* = (r − r0·5)/x. This is true for distributions in planes located as far downstream as two potential core lengths. The collapsed data of mean velocity can be approximated by a Görtler error function profile: \[ U/U_J = 0.5[1-{\rm erf}(\sigma\eta^{*})]. \] Centre-line distributions at various Mach numbers also collapse if plotted in terms of x/xc, xc being the potential core length. A general equation for the collapsed data of mean velocity is given by: U/UJ = 1 - exp{1.35/(1 - x/xc)}, for the range of Mach numbers 0·3-1·4, where xc = 4.2 + 1.1 MJ2.

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near-and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.

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The stability of three axisymmetric jet profiles is reviewed. These profiles represent the development of an incompressible jet from a nearly top-hat profile to a fully developed jet profile. The disturbance equations for arbitrary mode number in a region of zero shear, which provide the boundary conditions for the numerical solution, are solved analytically through use of the disturbance vorticity equations. Numerical solutions for the spatial stability for the axisymmetric (n= 0) disturbance and the asymmetricn= l disturbance are presented. Previously published calculations of least stable modes are shown to be incorrectly interpreted and their actual mode types are given. The critical Reynolds number is found to increase as the profile varies from a top-hat to a fully developed jet form. Closed contours of constant amplification, which are unusual in free shear flows, are shown to exist for then= 1 disturbance in the fully developed jet region. A fluctuation energy balance is used to justify the occurrence of this destabilizing effect of decreasing Reynolds number.

Broadband shock-associated noise is a component of jet noise generated by supersonic jets operating offdesign. It is characterized by multiple broadband peaks and dominates the total noise at large angles to the jet downstream axis. A new model is introduced for the prediction of broadband shock-associated noise that uses the solution of the Reynolds-averaged Navier-Stokes equations. The noise model is an acoustic analogy based on the linearized Euler equations. The equivalent source terms depend on the product of the fluctuations associated with the jet's shock-cell structure and the turbulent velocity fluctuations in the jet shear layer. The former are deterministic and are obtained from the Reynolds-averaged Navier-Stokes solution. A statistical model is introduced to describe the properties of the turbulence. Only the geometry and operating conditions of the nozzle need to be known to make noise predictions. This overcomes the limitations and empiricism present in previous broadband shock-associated noise models. Results for various axisymmetric circular nozzles and a rectangular nozzle operating at various conditions are compared with experimental data to validate the model.

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A fairly simple theoretical model of an anisotropic compliant wall has been developed. It has been used to undertake a comprehensive numerical study of boundary-layer stability over such walls. The study is based on linearized theory, makes the usual quasi-parallel-flow approximation, uses the Blasius profile as the basic undisturbed flow and assumes two-dimensional disturbances. An investigation is carried out of the effects of anisotropic wall compliance on the Tollmien–Schlichting waves and the two previously identified wall modes, namely travelling-wave flutter and divergence. In addition global convergence techniques are used to search for other possible instabilities.An asymptotic theory, valid for high Reynolds numbers, is also presented. This can provide accurate estimates of the eigenvalues. It is applicable to a much wider class of compliant walls than the relatively simple model used for the numerical study. An important use of the asymptotic theory is to help identify and elucidate the various energy-exchange mechanisms responsible for stabilization or destabilization of the instabilities. A reduction in the production of disturbance energy by the Reynolds shear stress is the main reason for the favourable effect of anisotropic wall compliance on instability growth. Other energy-exchange mechanisms, which have been found to make a significant contribution, include energy transfer from the disturbance to the mean flow due to the interaction of the fluctuating shear stress and the displaced mean flow, and the work done by the perturbations in wall pressure and shear stress.It is found that anisotropic wall compliance confers very considerable advantage with respect to reduction in instability growth rate and transition delay. Using a fairly conservative criterion an almost ten-fold rise in transitional Reynolds number is predicted for anisotropic walls having the appropriate properties. Anisotropic wall compliance makes travelling-wave flutter much more sensitive to viscous effects and has a considerable stabilizing influence. The application of global convergence methods has led to the discovery of an anomalous spatially growing eigenmode which, according to conventional interpretation, would represent an instability. Further study of an appropriate initial-value problem has revealed that the new eigenmode is probably not an instability and that, for compliant walls, complex wavenumbers with positive real and negative imaginary parts do not necessarily correspond to an instability.