Motivated by the phenomena of blocked and zonal flows in Earth's atmosphere, we conducted laboratory experiments and numerical simulations to study the dynamics of an eastward jet flowing over wavenumber-two topography. The laboratory experiments studied the dynamical behaviour of the flow in a barotropic rotating annulus as a function of the experimental Rossby and Ekman numbers. Two distinct flow patterns, resembling blocked and zonal flows in the atmosphere, were observed to persist for long time intervals.

Earlier model studies had suggested that the atmosphere's normally upstream-propagating Rossby waves can resonantly lock to the underlying topography, and that this topographic resonance separates zonal from blocked flows. In the annulus, the zonal flows did indeed have super-resonant mean zonal velocities, while the blocked flows appear subresonant. Low-frequency variability, periodic or irregular, was present in the measured time series of azimuthal velocity in the blocked regime, with dominant periodicities in the range of 6–25 annulus rotations. Oscillations have also been detected in zonal states, with smaller amplitude and similar frequency. In addition, over a large region of parameter space the two flow states exhibited spontaneous, intermittent transitions from the one to the other.

We numerically simulated the laboratory flow geometry in a quasi-geostrophic barotropic model over a similar range of parameters. Both flow regimes, blocked and zonal, were reproduced in the simulations, with similar spatial and temporal characteristics, including the low-frequency oscillations associated with the blocked flow. The blocked and zonal flow patterns are present over wide ranges of forcing, topographic height, and bottom friction. For a significant portion of parameter space, both model flows are stable. Depending on the initial state, either the blocked or the zonal flow is obtained and persists indefinitely, showing the existence of multiple equilibria.

We consider the motion of a finger of low-viscosity fluid as it propagates into a branching network of fluid-filled microchannels – a scenario that arises in many appli- cations, such as microfluidics, biofluid mechanics (e.g. pulmonary airway reopening) and the flow in porous media. We perform experiments to investigate the behaviour of the finger as it reaches a single bifurcation and determine under what conditions the finger branches symmetrically. We find that if the daughter tubes have open ends, the finger branches asymmetrically and will therefore tend to reopen a single path through the branching network. Conversely, if the daughter tubes terminate in elastic chambers, which provide a lumped representation of the airway wall elasticity in the airway reopening problem, the branching is found to be symmetric for sufficiently small propagation speeds. A mathematical model is developed to explain the experimentally observed behaviour.