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The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

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The variation of the lift coefficient in a symmetric airfoil (NACA 0012 profile) at very small angles of attack is studied experimentally and numerically for a range of low chord-based Reynolds numbers, Re. Experimentally, the non-linearity around the zero angle of attack leading to a switch in sign on the lift was observed for a big enough aspect ratio at Re = 40 × 103. The existence of the negative lift for wing models with the biggest aspect ratio suggests that the three-dimensional effects are negligible. Therefore, two-dimensional simulations were performed to understand the cause of the negative lift. For the cases with the negative lift, the flow displays an interesting feature of pre-alignment with the chord upstream of the profile. Furthermore, it was found that the negative lift is directly related to the positive net circulation (anti-clockwise) around the airfoil.