Vortices in oscillating spin-up

Laboratory experiments and numerical simulations of oscillating spin-up in a square tank have been conducted to investigate the production of small-scale vorticity near the no-slip sidewalls of the container and the formation and subsequent decay of wall-generated quasi-two-dimensional vortices. The flow is made quasi-two-dimensional by a steady background rotation, and a small sinusoidal perturbation to the background rotation leads to the periodic formation of eddies in the corners of the tank by the roll-up of vorticity generated along the sidewalls. When the oscillation period is greater than the time scale required to advect a full-grown corner vortex to approximately halfway along the sidewall, dipole structures are observed to form. These dipoles migrate away from the walls, and the interior of the tank is continually filled with new vortices. The average size of these vortices appears to be largely controlled by the initial formation mechanism. Their vorticity decays from interactions with other stronger vortices that strip off filaments of vorticity, and by Ekman pumping at the bottom of the tank. Subsequent interactions between the weaker ‘old’ vortices and the ‘young’ vortices result in the straining, and finally the destruction, of older vortices. This inhibits the formation of large-scale vortices with diameters comparable to the size of the container.The laboratory experiments revealed a $k^{-5/3}$ power law of the energy spectrum for small-to-intermediate wavenumbers. Measurements of the intensity spectrum of a passive scalar were consistent with the Batchelor prediction of a $k^{-1}$ power law at large wavenumbers. Two-dimensional numerical simulations, under similar conditions to those in the experiments (with weak Ekman decay), were also performed and the simultaneous presence of a $k^{-5/3}$ and $k^{-3-\zeta}$ (with $0\,