Various processes are described by which a drop of water, impacting on a water surface, may entrain a bubble. There are: (i) irregular entrainment, in which the complex details of a splash entrain bubbles; (ii) regular entrainment, in which the crater formed by the drop impact develops in a predictable way to form a single bubble; (iii) entrainment of large bubbles, in which most of the volume of the crater is trapped as a bubble; and (iv) Mesler entrainment, in which many very small bubbles are trapped in the very early stages of the impact process; possibly between wave crests of capillary waves which develop on the drop and on the water surface. This last process is different from the preceding three in that it produces very little sound. All of the processes except the third one have been described individually in the literature; here we present them together for comparison. The regular entrainment process is discussed in the greatest detail and some new experimental results are presented which concern the size and nature of the entrained bubbles. The significance of the regular and irregular entrainment processes to the generation of underwater sound by rain is discussed.

The evolution of a low-amplitude localized disturbance in a laminar boundary layer is considered. Linear inviscid theory illustrates that the disturbance may be divided into two parts: a dispersive wave part, represented by solutions to the Rayleigh equation which travel at their characteristic speeds, and a transient or advective part travelling at the local mean velocity. For a three-dimensional initial disturbance, calculations based on linear inviscid theory indicate that the transient portion of the disturbance does not decay and has the form of an inclined shear layer which elongates as the disturbance propagates downstream. The amplitude of the transient part exceeds by far that of the wave part of the disturbance. Experimental results are presented for a disturbance created by the impulsive motion of a small membrane flush-mounted at the wall. For small amplitudes, the initial evolution of the disturbance is found to be in good qualitative agreement with the inviscid calculations, showing the rapid formation of an inclined shear layer. Further downstream, the transient portion of the disturbance decays owing to viscous effects, leaving a linearly unstable dispersive wave packet. The evolutions of equal and opposite disturbances are compared and it is shown that, despite a weak nonlinearity that develops, the resultant wave packets are equal in structure but of opposite phase.

Navier–Stokes calculations were performed to simulate the evolution of a moderate-amplitude localized disturbance in a laminar flat-plate boundary layer. It was found that, in accordance with previous results for linear and weakly nonlinear disturbances, the evolving disturbance consists of two parts: an advective, or transient portion which travels at approximately the local mean velocity, and a dispersive wave portion which grows or decays according to Tollmien–Schlichting instability theory. The advective portion grows much more rapidly than the wave portion, initially linearly in time and, in contrast to the weak-disturbance case, gives rise to two distinct nonlinear effects. The first is a streamwise growth of the disturbed region producing a low-speed streak, bounded in the vertical and spanwise directions by intense shear layers. The second nonlinear effect is the onset of a secondary instability on the vertical shear layer formed as a result of spanwise stretching of the mean vorticity and giving rise to oscillations in the v- and w-components with a substantially smaller spatial scale than that of the initial disturbance. The effect of initial spanwise scale is assessed by calculating the disturbance for three different cases in which the spanwise scale and the initial disturbance amplitude were varied. It was found that the resulting perturbation depends primarily on the initial distribution of v in each plane z = const., but is approximately independent of the spanwise scale.

In a previous paper (Jensen & Pedley 1989) a model was analysed describing the effects of longitudinal wall tension and energy loss through flow separation on the existence and nature of steady flow in a finite length of externally pressurized, elastic-walled tube. The stability of these steady flows to small time-dependent perturbations is now determined. A linear analysis shows that the tube may be unstable to at least three different modes of oscillation, with frequencies in distinct bands, depending on the governing parameters; neutral stability curves for each mode are calculated. The motion of the separation point at a constriction in the tube appears to play an important role in the mechanism of these oscillations. A weakly nonlinear analysis is used to examine the instabilities in a neighbourhood of their neutral curves and to investigate mode interactions. The existence of multiple independent oscillations indicates that very complex dynamical behaviour may occur.

Recently Hall & Seddougui (1989) considered the secondary instability of large-amplitude Görtler vortices in a growing boundary layer into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. In the course of investigating the nonlinear version of this problem (Seddougui & Bassom 1990), we have found that the numerical work of Hall & Seddougui (1989) is incomplete; this deficiency is rectified here. In particular, we find that many neutrally stable modes are possible; we derive the properties of such modes in a high-wavenumber limit and show that the combination of the results of Hall & Seddougui and our modifications lead to conclusions which are consistent with the available experimental observations.

The linear stability of a viscous liquid sheet in the presence of ambient gas is investigated. It is shown that there are two independent modes of instability, sinuous and varicose. The large-time asymptotic amplitude of sinuous disturbances is found to be bounded but non-vanishing for all calculated values of Reynolds numbers and the gas-to-liquid density ratios when the Weber number is greater than one half. The Weber number We is defined as the ratio of the surface tension force to the inertia force per unit area of the gas–liquid interface. When We is smaller than one half, the sinuous mode is stable if the gas-to-liquid density ratio is zero, otherwise it is convectively unstable. The varicose mode is always convectively unstable unless the density ratio, Q, is zero. Then it is asymptotically stable. The spatial growth rate of the varicose mode is smaller than that of the sinuous mode for the same flow parameters. The wavelength of the most amplified waves in both modes is found to scale with the product of the sheet thickness and Q/We. It is shown, by use of the energy equation, that the mechanism of instability is a capillary rupture when We [ges ] 0.5, and the convective instability is due to the interfacial pressure fluctuation when We < 0.5.