Persistence and Evolution of Staircase Profiles

Staircases have been observed in drift-wave turbulence near marginal stability. We study staircase persistence and resiliency. The simplest type of staircase occurs in passive scalar advection by an array of convection cells, due to the existence of two disparate time scales, the cell turn-over and the diffusion times. To better represent physics of dynamic drift-wave turbulence, we adopt a novel model of a fluctuating vortex array as a basis for a series of numerical experiments. By systematically scattering the elements of the vortex array, we show that staircase profiles form and are resilient over a broad range of modest Reynolds numbers. We find that scalar concentration flows around vortices, thus staircase barriers form first and scalar concentration “homogenizes” in vortices later. The effective diffusivity for the perturbed vortex array does not deviate significantly from that for a fixed cellular array. Slight deviations are the result of changes in cell geometric properties. We also examine the case of active scalar staircase formation. The dynamics of the active scalar are comparable to that of magnetic fields in flux expulsion, where fields are expelled to cell boundaries and stabilize the staircase cells. The active scalar system manifests a novel feedback mechanism that reinforces global staircase structure and self-organization. We show that the spontaneous reinforcement of the cell array structure in the presence of fluctuations occurs only for a narrow range of magnetic field strength.