In the context of rotating geophysical flows, the presence of variable topography affects the motion of intense vortices and promotes the generation of new vortical structures. In this study, the quasi-two-dimensional dynamics of such systems is examined with numerical simulations and analytical models. The results are discussed from two points of view. First, the motion of a barotropic, dipolar vortex encountering a submarine mountain is analysed, with an emphasis on the modification of the trajectory and dipole structure when passing over the topography. For relatively low mountains, the vortex path is deflected towards the anticyclonic side of the dipole owing to squeezing effects (as the anticyclone becomes more intense than the cyclonic part). For higher mountains, the dipole splits into two parts; the anticyclone pairs with newly formed positive vorticity (generated by the stretching fluid moving downhill), while the cyclone remains trapped near the summit. These results are discussed using modulated point-vortex models. Second, the long-lived residual flows over the topography are studied. The most conspicuous cases are asymmetric dipolar vortices, which remain confined on the summit while rotating clockwise. The formation of new dipoles arises from the combination of nonlinear motions and topographic Rossby waves around the mountain. The results are illustrated with new analytical solutions of nonlinear dipoles over mountains.

The relaxation of turbulent pipe flow downstream of a single square bar roughness element is studied at distances up to $120R$ ($R$ is the pipe radius). Three bar heights, $h/R = 0.04$, 0.1 and 0.2, are investigated. The data suggest three stages for the relaxing flow. Immediately following the square bar is the development of a separated shear layer, where we find that the peak Reynolds stress scales linearly with $h/R$ and the disturbance profile is characterised by $h$. The bulk shear stress and turbulence intensity in this stage scale as $(h/R)^{2}$ and reach their maximum near the reattachment point. The second stage features the redistribution of turbulence towards the pipe centre and a power law in the decay of turbulence. The extent of this region is characterised by a streamwise length scale, ${x_c}$, which measures the extent of the redistribution process. The final stage of recovery is found to be long-lasting and oscillatory owing to asynchronous recovery between the mean velocity and the Reynolds stress. The oscillation wavelength scales with ${x_c}$ and decreases with increasing $h/R$. In contrast, the deficits in the mean shear and the bulk shear stress increase with $h/R$. For all three bar sizes, the flow recovery is not complete until the streamwise distance exceeds 500$h$–1000$h$.

The present paper reports on a time-resolved three-dimensional experimental study of turbulent Rayleigh–Bénard convection inside a cylinder with one-half aspect ratio. The working fluid is water and the Rayleigh and Prandtl numbers are, respectively, $1.86\times 10^{8}$ and $7.6$. Measurements are carried out via time-resolved particle tracking velocimetry for a relatively long time (approximately four hours) and due to the limited size of the convection cell (internal diameter of $74$ mm) the whole interior of the cylindrical sample is investigated. This allows a proper analysis of the statistical behaviour of the flow across the time. Proper orthogonal decomposition (POD) is used to extract the characteristic modes of the turbulent thermal convection. It is shown that the low-order POD modes are strictly related to the formation of a large scale circulation (LSC) and its organization in a single-roll state (SRS) or a double-roll state. Innovative criteria for the identification of the instantaneous flow state based on the POD analysis are also proposed. Such criteria are proved to overcome the limitations of methods commonly adopted in the previous literature and relying on the analysis of the azimuthal profiles of the temperature or the vertical velocity at three different heights (one quarter, one half and three quarters of the cell height). Compared with the latter methods, the POD-based criteria identify a larger frequency of occurrence of the SRS, which is recognized as the most frequent state of the LSC in the investigated conditions.