Inhomogenous Mixing and the Fundamentals of Layering and Staircases

Layered structures — often referred to as staircases — are ubiquitous. The many hypotheses for the mechanism of layering lead one to attempt to realize the simplest possible path to the formation of layered structure. More specifically, one also aims to understand how layered structures escape the predicted fate of homogenization. To this end, we examine the physics of passive scalar mixing in a bistable Cahn–Hilliard–Navier–Stokes cell. We show how the system first undergoes piecewise homogenization, in which deviation from uniformity is first reduced to a finite number of asymptotically small domain walls. These subsequently mix to a homogenous state on long time scales. This analysis shows that layering does not depend on elaborate feedback processes.