Friction-induced scale-selection in the extended Cahn-Hilliard model for zonal staircase

In this work, we describe a possible mechanism to set the radial scale of zonal flows, which may be applicable to the E B staircase found in the global full-f simulations such as G. Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015). 1D numerical simulation results of the Cahn-Hilliard model - extended to include zonal flow friction - can be understood from a heuristic nonlinear analysis. The staircase step-size Δ is found to decrease as the dimensionless zonal flow friction μ increases. It scales like Δ μ^α, with α -0. 41, up to a constant offset.