Results of experiments on the low-Reynolds-number flow of liquid drops through a horizontal circular tube with a diameter that varies sinusoidally with axial position are reported. Measurements of the contribution of the drop to the local pressure gradient and the relative velocity of the drop are correlated with the time-dependent drop shape. Both Newtonian and viscoelastic suspending fluids are considered. The viscosity ratio, volumetric flow rate and drop size are varied in the experiment, and both neutrally buoyant and non-neutrally buoyant drops are studied. Comparison with previous results for a straight-wall tube shows that the influence of the tube boundary geometry on the drop shape is substantial, but the qualitative effect of the tube shape depends strongly on the relative importance of viscous forces compared to interfacial tension for the particular experiment. For Newtonian fluids, two modes of drop breakup, which are distinguished by the magnitude of the viscosity ratio, are observed. When the suspending fluid is viscoelastic, both shear-thinning and time-dependent rheological effects are present.

Density currents in a rotating fluid are produced by releasing a volume of buoyant fluid from a lock at one end of a long rotating channel. Coriolis forces hold the current against one wall. It is observed that the velocity and depth of the nose decrease exponentially in time, implying that the nose can effectively come to a halt at a finite distance from the lock. In reality though, the flow regime eventually changes and a viscous wedge-shaped intrusion continues. The high-Reynolds-number currents contain three-dimensional turbulence a short distance behind the nose, but the influence of rotation causes this to become quasi-two-dimensional further upstream. The intrusion and turbulent motions represent a forcing to the lower layer that produces vortex and wave-like motions which penetrate deep into the lower-layer fluid. It is shown that the exponential decay can be attributed to radiation of momentum by these inertial waves.

The width l of the turbulent current varies with distance behind the nose, from 0.6 times the local time-dependent deformation radius at the ‘head’ to l ≈ R0 far upstream, where R0 is the initial deformation radius in the lock. The nose of the boundary current is unstable, with billows appearing near the tip of the intruding nose and leading to an intermittent breakup of the ‘head’ structure and oscillations of the nose velocity. These oscillations are rapid, often having frequencies much greater than f (where f = 2Ω is the Coriolis parameter), and, along with the production of the turbulence that is so characteristic of the currents, are attributed to a Kelvin–Helmholtz instability. Rotationally dominated baroclinic waves appear only a very large distance behind the nose.

The behaviour of granular material in motion is studied from a continuum point of view. Insofar as possible, individual grains are treated as the ‘molecules’ of a granular ‘fluid’. Besides the obvious contrast in shape, size and mass, a key difference between true molecules and grains is that collisions of the latter are inevitably inelastic. This, together with the fact that the fluctuation velocity may be comparable to the flow velocity, necessitates explicit incorporation of the energy equation, in addition to the continuity and momentum equations, into the theoretical description. Simple ‘microscopic’ kinetic models are invoked for deriving expressions for the ‘coefficients’ of viscosity, thermal diffusivity and energy absorption due to collisions. The ‘coefficients’ are not constants, but are functions of the local state of the medium, and therefore depend on the local ‘temperature’ and density. In general the resulting equations are nonlinear and coupled. However, in the limit s [Lt ] d, where s is the mean separation between neighbouring grain surfaces and d is a grain diameter, the above equations become linear and can be solved analytically. An important dependent variable, in this formulation, in addition to the flow velocity u, is the mean random fluctuation (‘thermal’) velocity $\overline{v}$ of an individual grain. With a sufficient flux of energy supplied to the system through the boundaries of the container, $\overline{v}$ can remain non-zero even in the absence of flow. The existence of a non-uniform $\overline{v}$ is the means by which energy can be ‘conducted’ from one part of the system to another. Because grain collisions are inelastic, there is a natural (damping) lengthscale, governed by the value of d, which strongly influences the functional dependence of $\overline{v}$ on position. Several illustrative examples of static (u = 0) systems are solved. As an example of grain flow, various Couette-type problems are solved analytically. The pressure, shear stress, and ‘thermal’ velocity function $\overline{v}$ are all determined by the relative plate velocity U (and the boundary conditions). If $\overline{v}$ is set equal to zero at both plates, the pressure and stress are both proportional to U2, i.e. the fluid is non-Newtonian. However, if sufficient energy is supplied externally through the walls ($\overline{v} \ne 0$ there), then the forces become proportional to the first power of U. Some examples of Couette flow are given which emphasize the large effect on the grain system properties of even a tiny amount of inelasticity in grain–grain collisions. From these calculations it is suggested that, for the case of Couette flow, the flow of sand is supersonic over most of the region between the confining plates.

The ‘whistler nozzle’ is a simple device which can induce jet self-excitations of controllable amplitudes and frequencies and appears highly promising for many applications involving turbulent transport, combustion and aerodynamic noise. This paper documents the characteristics of this curious phenomenon for different values of the controlling parameters and explains the phenomenon. It is shown that the whistler excitation results from the coupling of two independent resonance mechanisms: shear-layer tone resulting from the impingement of the pipe-exit shear layer on the collar lip, and organ-pipe resonance of the pipe nozzle. The crucial role of the shear-layer tone in driving the organ-pipe resonance is proven by reproducing the event in pipe–ring and pipe–hole configurations in the absence of the collar. It is also shown that this phenomenon is strongest when the self-excitation frequency matches the ‘preferred mode’ of the jet.

The ‘whistler-nozzle’ phenomenon occurs for both laminar and turbulent initial boundary layers; the excitation can be induced without the pipe nozzle (say, by ring or hole tone) when the exit flow is laminar but not when it is turbulent. Unlike the shear-layer tone and jet tone phenomena, where successive stages overlap, adjacent stages of the whistler-nozzle excitation are separated by ‘dead zones’ where the conditions for both resonance mechanisms cannot be simultaneously met. Also, unlike the shear-layer and jet tones, the whistler frequency cannot be varied continuously by changing the speed. Since the phenomenon is the coupling of two resonance mechanisms, the frequency data appear to defy a simple nondimensional representation for the entire range of its operation. Reasonable collapse of data is achieved, however, when the exit momentum thickness is used as a lengthscale, thus emphasizing the role of the shear-layer tone in the phenomenon.