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We consider the effects of strong critical-layer nonlinearity on the spatially growing instabilities of a shear layer between two parallel streams. A composite expansion technique is used to obtain a single formula that accounts for both shear-layer spreading and nonlinear critical-layer effects. Nonlinearity causes the instability to saturate well upstream of the linear neutral stability point. It also produces vorticity roll-up that cannot be predicted by linear theory.

The effect of viscosity on the capillary instability of a liquid jet is examined. The critical Weber number for convective instability is determined as a function of Reynolds number and comparison is made with the inviscid limit. It is shown that certain waves that are neutral in the inviscid case exhibit growth for finite Reynolds numbers.

This paper is concerned with utilizing the acoustic analogy approach to predict the sound from unheated supersonic jets. Previous attempts have been unsuccessful at making such predictions over the Mach number range of practical interest. The present paper, therefore, focuses on implementing the necessary refinements needed to accomplish this objective. The important effects influencing peak supersonic noise turn out to be source convection, mean flow refraction, mean flow amplification, and source non-compactness. It appears that the last two effects have not been adequately dealt with in the literature. The first of these because the usual parallel flow models produce most of the amplification in the so called critical layer where the solution becomes singular and, therefore, causes the predicted sound field to become infinite as well. We deal with this by introducing a new weakly non parallel flow analysis that eliminates the critical layer singularity. This has a strong effect on the shape of the peak noise spectrum. The last effect places severe demands on the source models at the higher Mach numbers because the retarded time variations significantly increase the sensitivity of the radiated sound to the source structure in this case. A highly refined (non-separable) source model is, therefore, introduced in this paper.

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The coupling between imposed disturbances and capillary instabilities on a liquid jet is examined. It is shown that in most physical situations the forcing produces neutral waves which can then turn into growing waves as the profile relaxes or may be amplified nonlinearly by a mechanism of the type considered by Akylas & Benney (1980). The effectiveness of the coupling is expressed quantitatively by numerically computed values of the ‘coupling coefficient’.

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams. The analysis shows that mean temperature non-uniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integro-differential equation which bears some resemblance, to the Landau equation in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that inviscid solutions always end in a singularity at a finite downstream distance but that viscosity can eliminate this singularity for certain parameter ranges.