Jet Hysteresis in a Simple QG Model

Zonal jets are a feature common to rotating planets, and are prevalent in the Southern Ocean (SO) and planetary atmospheres. In the extratropics, zonal jets are maintained through convergence of momentum driven by meridionally propagating Rossby waves into latitudes with baroclinic instability. The formation and persistence of jets under these conditions has been extensively studied in simple and complex models. The strength and spacing of jets are determined by a variety of model parameters, including the gradient of planetary vorticity (β), frictional terms, wind stress (for the ocean), and topography. While numerous studies have explored how these parameters affect jet strength and spacing in statistically steady simulations, less attention has focused on transitions between different equilibrium states in response to changes in these parameters.

Here we consider the effect of a temporally varying bottom friction on jet strength and spacing. We use a two-layer quasi-geostrophic (QG) model in a doubly periodic domain on a beta plane, with a rigid lid and flat topography. The model is spun up with constant β and bottom friction (κ). Once the model has equilibrated, we vary κ in two ways: (1) a step-change (increase or decrease) or (2) a linear increase or decrease. In (1), an increase in friction leads to a re-organization of the jet structure. The transition period involves a weakening of existing jets, as well as increased meandering associated with the formation of new jets. However, a subsequent decrease in bottom friction to its original value does not result in the jets returning to their original structure. Instead, the new jet structure persists and strengthens. Thus hysteresis occurs with respect to jet spacing and bottom friction. We also (2) consider a linear increase or decrease in κ, which leads to the same qualitative results. However, we can now follow the temporal evolution of jet structure changes. In the case of increasing κ, a threshold value is reached, at which point the jet structure re-organizes. We find that the jets continuously weaken (strengthen) as κ increases (decreases). Just before the jets re-organize, we see a sharp increase in eddy strength, indicating these abrupt transitions in jet structure are mediated by eddies. We discuss the role of eddy potential vorticity (PV) fluxes in facilitating these transitions through modifications in Reynolds stress divergence and the anisotropy of coherent mesoscale eddies.