UC San Diego

This paper presents a theory for the formation and evolution of coupled density staircases and zonal shear profiles in a simple model of drift-wave turbulence. Density, vorticity, and fluctuation potential enstrophy are the fields evolved in this system. Formation of staircase structures is due to inhomogeneous mixing of generalized potential vorticity (PV), resulting in the sharpening of density and vorticity gradients in some regions, and weakening them in others. When the PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps,” and “steps,” which are, respectively, the regions of local gradient steepening and flattening. The jumps merge and migrate in radius, leading to the development of macroscale profile structures from mesoscale elements. The positive feedback process, which drives the staircase formation occurs via a Rhines scale dependent mixing length. We present extensive studies of bifurcation physics of the global state, including results on the global flux-gradient relations (flux landscapes) predicted by the model. Furthermore, we demonstrate that, depending on the sources and boundary conditions, either a region of enhanced confinement, or a region with strong turbulence can form at the edge. This suggests that the profile self-organization is a global process, though one which can be described by a local, but nonlinear model. This model is the first to demonstrate how the mesoscale condensation of staircases leads to global states of enhanced confinement.