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 in Dif-Pradalier et al., [Phys. Rev. Lett. 114, 085004 (2015)0031-900710.1103/PhysRevLett.114.085004]. One-dimensional 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∼logμ^{α}, with α≃-0.41, up to a constant offset.