Experiments have shown that a large-eddy breakup device consisting of a short splitter plate placed in the turbulent boundary layer over a plane wall can lead to a reduction in drag. We investigate the idealized problem of an incident line vortex convected past such a device. The vorticity shed from the trailing edge of the plate is found to cancel the effect of the incident vortex and to reduce velocity fluctuations significantly in the vicinity of the wall.

Both the incompressible and supersonic laminar flow over a small, unsteady hump are considered. The Reynolds number is assumed large, and the analysis is based upon triple-deck theory. In the incompressible case disturbances tend to grow downstream, as a result of triggering the Tollmien–Schlichting mode of instability. For the supersonic case the flow disturbances tend to decay downstream across the entire frequency spectrum. However, for sufficiently large humps a seemingly catastrophic failure of the governing equations may occur, our results suggesting that this is caused by an inviscid, short-scale, Rayleigh type of instability.

An initial-value problem is considered for the oceanographically relevant case of slow flow over obstacles of small height and horizontal scale of order the fluid depth or larger. Previous work on starting flow over obstacles whose contours are closed (Johnson 1984) is extended to flow forced by a source–sink pair to cross a step change in depth bounded by a vertical sidewall. Bottom contours thus end abruptly and the near-periodic solutions of the earlier work are no longer possible. The relevant timescale for the motion is again the topographic vortex-stretching time h/2Ωh0, where h is the fluid depth, Ω the background rotation rate and h0 the step height. This time is taken to be long compared with the inertial period but short compared with the advection time. It is shown that if shallow water lies to the right (looking away from the wall) a wavefront moves outwards exponentially fast leaving behind a flow equivalent to that obtained by replacing the step by a rigid wall. If shallow water lies to the left the wavefront approaches the wall, forming at the wall–step junction an unsteady, exponentially thinning, singular region that transports the whole flux. The relevance of these solutions to experiments and steady solutions for free-surface and two-layer flows in Davey, Gill, Johnson & Linden (1984, 1985) is discussed.

In this paper the translatory motion of a compound drop is examined in detail for low-Reynolds-number flow. The compound drop, consisting of a liquid drop or a gas bubble completely coated by another liquid, moves in a third immiscible fluid. An exact solution for the flow field is found in the limit of small capillary numbers by approximating the two interfaces to be spherical. The solution is found for the general case of eccentric configuration with motion of the inner sphere relative to the outer together with the motion of the system in the continuous phase. The results show that the viscous forces tend to move the inner-fluid sphere towards the front stagnation point of the compound drop. For equilibrium of the inner sphere with respect to the outer there must, therefore, be a body force towards the front. This can only be achieved with the necessary condition that there be a buoyant force on the inner sphere, opposite to that of the compound drop in the continuous phase. For a given set of fluids, two or four equilibrium configurations may be found. Of these only one or two, respectively, are stable. The others are unstable. For the special case of concentric configuration, the equilibrium is always metastable.