In this paper the normal-mode small-amplitude waves of high-speed jets are investigated analytically and computationally. Three families of instability waves, each having a distinct wave pattern and propagation characteristics, have been found. One of the families of waves is the familiar Kelvin-Helmholtz instability wave. The other two families of waves do not appear to have been clearly identified and systematically studied before. Waves of one of the new wave family propagate with supersonic phase velocities relative to the ambient gas. They are, therefore, referred to as supersonic instability waves. Waves of the other family have subsonic phase velocities. Accordingly they are called subsonic waves. The subsonic waves have the unusual property that they are unstable only for jets with finite thickness mixing layers. They are neutral waves when calculated by a vortex-sheet jet model.

Earlier Oertel (1979, 1980, 1982) using a novel optical technique observed in a series of experiments three sets of waves in high-speed jets. The origin of these waves, however, remains so far unexplained and a theory has yet to be developed. In the present study it will be shown that the computed wave patterns and propagation characteristics of the Kelvin-Helmholtz, the supersonic and the subsonic instability waves match essentially those observed by Oertel. The physical mechanisms which give rise to the three families of waves as well as some of the most salient characteristic features of each set of waves are discussed and reported here.

The initial unsteady two-dimensional flow around an impulsively started circular cylinder is investigated using the random-vortex numerical method. To understand the mechanisms of the primary and secondary vortex formation, we investigate the relationship between the creation, diffusion and convection of vorticity to the genesis and evolution of the complex and ‘unstable’ flow structures of the recirculating zone behind the cylinder. Our simulation reveals detailed geometric features of the wake which are in agreement with experimental observations and with other numerical calculations. Numerical calculation at Reynolds numbers R = 3000, 9500 and 104 show that the numerical method is appropriately sensitive to changes of the Reynolds number. Numerical functionals such as the length of the wake, velocity on the wake axis and the angle of separation for our calculations are in satisfactory agreement with known experimental and numerical results. This numerical method gives results comparable to those of a previously published method but does so using much less memory and computer time.

Convection rolls in a fluid layer heated from below become unstable to disturbances in the form of waves travelling along the axis of the rolls when the Rayleigh number exceeds a critical value RII. This transition to a time-dependent form of convection also occurs in the presence of a vertical magnetic field when the fluid is electrically conducting. In this paper the finite-amplitude properties of these waves are investigated for the values 0.1 and 0.025 of the Prandtl number. It is shown that the onset of oscillations reduces the heat transport by convection and that a mean flow in the direction of propagation is associated with the waves. Although the magnetic field has an inhibiting influence on steady convection, the inhibiting influence on the onset of oscillations is even stronger such that in some cases a higher heat transport is obtained in the presence of a magnetic field than in its absence. For similar reasons subcritical finite-amplitude onset of travelling-wave convection occurs for sufficiently large magnetic field strengths. Finally the stability of travelling-wave convection is investigated and the Rayleigh number RIII for the transition to asymmetric wave convection is determined.

On a linearized theory, the pressure field due to bubbles oscillating asymmetrically in a ‘distortion mode’ decays with radial distance r like r−(n+1), where n > 1. Hence these modes have been thought to produce a negligible emission of sound. In this paper it is shown that, on the contrary, in nonlinear theory the distortion modes produce a monopole radiation of sound (n=0) at second order. Its frequency is twice the basic frequency of the distortion mode, and the sound amplitude is proportional to the square of the distortion amplitude. The magnitude of the pressure fluctuations within the bubble is comparable with 1 atmosphere.

In Part 1 it was shown that an asymmetric, normal-mode bubble oscillation will emit monopole radiation at second order. Here we show that a general initial distortion of the bubble, with no initial volume change, can be resolved into normal modes each of which radiates independently. The zero-order ‘breathing mode’ is stimulated also.

Because of the peculiar damping characteristics, and the possibility of a resonance between the distortion modes and the breathing mode, the pulse of sound produced by the initial distortion will appear to have approximately the fequency of the breathing mode.

The conclusions are borne out in some detail by a comparison with the experiments of Fitzpatrick & Strasberg (1957) on the underwater sound generated by bubbles breaking away from a nozzle. A similar mechanism may contribute significantly to the generation of sound at the sea surface.