Potential vorticity fronts and the late-time evolution of large-scale quasi-geostrophic flows

The late-time behaviour of freely evolving quasi-geostrophic flows with initial characteristic length scale $L_0$ larger than or equal to the deformation radius $L_D$, $L_0/L_D \geq 1$, is studied. At late time the flows are dominated by large multi-level vortices consisting of ascending terraces of well-mixed potential vorticity (PV), i.e. PV staircases. We examine how the number of mixed PV levels depends on the initial conditions, in particular $L_0/L_D$. For sufficiently large values of $L_0/L_D \approx 5$, a complete staircase with regular steps forms, but as $L_0/L_D$ decreases, the staircase becomes more irregular, with fewer mixed levels and the appearance of a large step centred on zero PV, corresponding to large regions of near-zero PV separating the multi-level vortices. This occurs because weak PV features in the initial field with scales smaller than $L_D$ undergo filamentation and are coarse-grained away or homogenised. For all values of $L_0/L_D$ considered, inverse cascades of potential energy commence at sufficiently late times. The onset of these cascades, even when the flow is initialised well within the ‘asymptotic model’ (AM) regime, suggests that the AM regime is not self-consistent: when potential vorticity fronts are well-resolved, frontal dynamics eventually drive ongoing flow evolution.