Staircase Formation by an Array of Stationary Convective Cells

We show that a staircase profile of scalar concentration forms in a simple system of stationary convective cells set in a fixed array. This case study is a particularly simple example of layer formation. Here, for Peclet number much greater than one, layering results from the interplay of the two disparate time scales in the problem, namely the cell turn-over time and the diffusion time. They key physics is that cell-to-cell transport is controlled by diffusion, and thus slow. This system has properties in common with those with richer dynamics near marginality. We study staircase resilience by exploring the consequences of imposing: i.) a spatially varying cross-profile shear flow (N.B. The shearing rate introduces a third time scale) and ii.) noisy concentration deposition and the consequent stochastic avalanching. Results concerning the response of the staircase structure will be discussed.