When a salt-stratified body of fluid is heated from the side a series of almost horizontal convective layers can develop with well-mixed interiors. These layers can propagate into the interior of the stratified fluid. This behaviour is also observed with intrusions at fronts between stratified bodies of fluid where their composition varies. We look at a simplified model of intrusion growth where the mechanism behind the creation of their well-mixed interiors is neglected, and look at how a stack of such intrusions will propagate away from the wall or front. We find that there is a transition from a regime where the propagation is essentially inviscid and the intrusion length is proportional to time, to one where viscosity is important and the propagation rate slows down, with the length being proportional to the square-root of time.

The complex flow features that arise from the impact of a shock wave on a concave cavity are determined by means of high-speed video photography. Besides additional information on features that have previously been encountered in specific studies, such as those relating to shock wave reflection from a cylindrical wall and those associated with shock wave focusing, a number of new features become apparent when the interaction is studied over longer times using time-resolved imaging. The most notable of these new features occurs when two strong shear layers meet that have been generated earlier in the motion. Two jets can be formed, one facing forward and the other backward, with the first one folding back on itself. The shear layers themselves develop a Kelvin–Helmholtz instability which can be triggered by interaction with weak shear layers developed earlier in the motion. Movies are available with the online version of the paper.

Centre-of-mass motions of two coupled spherical-cap droplets are considered. A model with surface tension and inertia that accounts for finite-amplitude deformations is derived in closed form. Total droplet volume λ and half-length L of the tube that connects the droplets are the control parameters. The model dynamics reside in the phase-plane. For lens-like droplets λ < 1, and for any L there is a single steady state about which the droplets vibrate with limit-cycle behaviour. For λ>1, the symmetric state loses stability (saddle point) and new antisymmetric steady states arise about which limit-cycle oscillations occur. These mirror states – big-droplet up or big-droplet down – are also stable. In addition, there are large finite-amplitude ‘looping’ oscillations corresponding to limit cycles that enclose both steady states in the phase-plane. All three kinds of oscillations are documented in an experiment that sets the system into motion by ‘kicking’ one of the droplets with a prescribed pressure-pulse. Model predictions for frequencies are consistent with observations. Small-amplitude predictions are placed in the wider context of constrained Rayleigh vibrations. A model extension to account for the small but non-negligible influence of viscosity is also presented.