The subject of the present study is the question of how the sound power of a jet of constant exit velocity would vary if the jet exit density were varied. Changes in jet exit density would inevitably be accompanied in a real experiment by changes in the speed of sound (temperature) in the jet, so that both effects must be considered simultaneously. The point of view advanced at the end of the study is that experimentally observed results in this area seem to admit an explanation based on how the radiative efficiency of moving acoustic sources is affected by the shrouding effect of a jet flow whose velocity, temperature and density differ from those of the ambient fluid. This change in efficiency is calculated with the aid of a simple model as follows. We determine the acoustic power output of a convected monopole source, simple harmonic in its own frame of reference, moving along the axis of a plug-flow round jet whose velocity is the same as that of the source. The jet is doubly infinite and the source is assumed to have an infinite lifetime. The density and temperature of the jet are allowed to differ from those of the ambient fluid though the specific-heat ratio of the jet fluid is assumed to be the same as that of the ambient. The requirement of equality of the static pressure inside and outside the jet then calls for a certain restraint on how the jet density and temperature vary. For a specific value of the jet exit velocity, the variation of acoustic power with the ratio of jet to ambient density along with a simple assumption on how the source strength varies with jet density are employed to deduce theoretically the ‘jet density exponent for jets which are subsonic with respect to the ambient speed of sound. The jet density exponent is found to depend both on the jet Mach number and even more strongly on a source frequency parameter. The theoretical results are compared with some experimental studies of this problem. Encouraging agreement is obtained both for the detailed observed effects on the power spectrum and the exponent for the overall power.

An analytical study is made of simple models of steady fronts in the atmosphere in which the temperature field is subjected to deformation as the fluid moves downstream in a large-scale horizontal flow. One fundamental approximation is made and then a Lagrangian method, in which fluid particles are identified by conservation of entropy and potential vorticity, and by Bernoulli's theorem, enables the steady problem to be solved. Solutions for models of surface fronts and upper tropospheric fronts are compared with those obtained from a model in which there is no variation along the front and the frontogenesis proceeds in time. If the thermal wind is comparable with the basic wind, and the potential vorticity is not negligible in some sense, the frontogenesis is increased where the thermal wind opposes the basic flow but, decreased where it reinforces the flow.

The interaction between an acoustic source, an unstable shear layer and a large inhomogeneous solid surface is studied, using an idealized model in which a vortex sheet is generated by uniform subsonic flow on one side of a semi-infinite plate, and subjected to line-source irradiation. Both the steady-state (time-harmonic) and initial-value (impulsive source) situations are examined. In particular, the time-harmonic field which can develop in a causal manner from a quiescent initial state is examined, and a specific criterion is given by which one may obtain the correct causal harmonic solution without explicit consideration of an initial-value problem. The satisfaction of this criterion demands not only the presence in the harmonic problem of the Helmholtz instability of an infinite vortex sheet (Jones & Morgan 1972), but additionally the presence of an edge-scatttered instability which in real time consists of a singular line plus a tail. The harmonic solution is discussed in some detail, and the consequences of omitting the unstable solutions and thereby violating causality are shown greatly to affect the diffracted field in some circumstances. The general features of the initial-value problem are also dealt with, the various waves being classified and their arrival times at any point being given in simple form. The paper ends with some speculations as to the applicability of these phenomena to the description of the process of ‘parametric amplification’, by which sound generated within a duct can be greatly amplified in the far field by triggering unstable modes on the shear layer shed from the duct.

Two-species, irreversible, very rapid reactions, with mild heat release, in a turbulent shear flow are shown to be analogous to the transport of two non-reacting species by the same shear field. Expressions for the probability density functions of the reacting species, the product species and the reaction-generated thermal field are obtained in terms of the joint probability density functions of the two nonreacting species. As an example we have constructed, from recent measurements of temperature statistics at a cross-section in a heated jet, the meanand fluctuating concentration fields of the reacting species and the mean concentration of the product.