The linearized equations of motion show that in a viscous heat-conducting compressible medium three modes of fluctuations exist, each one of which is a familiar type of disturbance. The vorticity mode occurs in an incompressible turbulent flow, the entropy mode is familiar as temperature fluctuations in low speed turbulent heat transfer problems, and the sound mode is the subject of conventional acoustics. A consistent higher order perturbation theory is presented with the only restrictions being that the Prandtl number is 3/4 and the viscosity and heat conductivity are monotinic functions of the temperature alone. The theory is based on expansion of the disturbance fields in powers of an amplitude parameter α. The non-linearity of the full Navier-Stokes equations can be interpreted as interaction between the three basic modes; in order to help physical insight the interactions are classed as ‘mass-like’, ‘force-like’, and ‘heat-like’ effects.Besides the amplitude parameter α there is another subsidiary non-dimensional parameter ε which indicates the relative importance of viscosity and heat conduction effects as compared to the inertial effects, ε is proportional to the ratio of the molecular mean free path and the characteristic length of the flow pattern (Knudsen number). The main contribution of the paper is the outline of a consistent successive approximation for an arbitrary order in α and the presentation of explicit formulae for the second order (bilateral) interactions.A special case of rather general significance is treated in more detail. This is when all three basic modes have intensities and length scales of the same orders of magnitude and in addition to α the parameter ε is also small; the second-order interactions are then relatively few and easily identifiable and are shown in table 1.The present analysis also sheds some light on the ‘zero order’ approximation which treats the vorticity and entropy disturbances as a ‘frozen pattern’ and the sound field as propagating nondissipative waves. The interpretation of hot-wire measurements relies heavily on these simplified models and the present paper lends some support to these current hot-wire practices.

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The second-order force produced by a sound beam directed normally at a plane target is calculated. Previous theories on acoustic radiation pressures associated with plane acoustic waves are examined critically and erroneous results, where they exist, are noted and rectified. A number of general relations are established using a new approach which avoids the necessity of dealing with detailed solutions of the governing nonlinear equations. Some of the concepts inferred from known solutions obtained by previous authors require drastic revision in the light of the present study. Specifically, the notion that Rayleigh radiation pressure depends on the nonlinearity of the medium (while Langevin radiation pressure does not) is not true in the case where the medium is bound by a partially reflecting wall. Again, that the concept that Rayleigh radiation pressure depends on the acoustic field only through the energy density of the field is shown to be false. In one instance it is shown to depend also on how the field is maintained, while in another instance it does not appear to depend on the mean energy density of the field at all.

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The second-order force produced by a sound beam directed normally at a plane target is calculated. Previous theories on acoustic radiation pressures associated with plane acoustic waves are examined critically, and erroneous results, where they exist, are noted and rectified. A number of general relations are established using a new approach which avoids the necessity of dealing with detailed solutions of the governing nonlinear equations. Some of the concepts inferred from known solutions obtained by previous authors require drastic revision in the light of the present study. Specifically, the notion that Rayleigh radiation pressure depends on the nonlinearity of the medium (while Langevian radiation pressure does not) is not true in the case where the medium is bounded by a partially reflecting wall. Again, the concept that the Rayleigh radiation pressure depends on the acoustic field only through the energy density of the field is shown to be false. An example is given showing that it depends also on how the field is maintained. [Work supported by Physics Program, ONR.]

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Shadowgraph studies of the explosive vaporization of a transparent water droplet after irradiation by a high intensity beam show that dielectric breakdown occurs within the droplet shadow face and generates a dense plasma, which absorbs the laser pulse. The convective forces expel the vapor from the droplet shadow face. We have deduced (1) the vapor propagation velocities, (2) the recoil velocity of the remaining droplet, and (3) the deformation rate of the illuminated face. Droplets are noted to eject fingerlike material from the surface facing the single laser-vaporized droplet when the asymmetrical vapor intercepts the neighboring droplets.