Structures, profile consistency, and transport scaling in electrostatic convection

Abstract

Two mechanisms at the origin of profile consistency in models of electrostatic turbulence in magnetized plasmas are considered. One involves turbulent diffusion in collisionless plasmas and the subsequent turbulent equipartition of Lagrangian invariants. By the very nature of its definition, this state can only be reached in the absence of imposed fluxes of the transported quantities. As such, the concept of turbulent equipartition cannot be used to interpret profiles in numerical simulations of interchange modes, as it has nevertheless been done in the past. It is shown in this article that for interchange modes, profile consistency is in fact due to mixing by persistent large-scale convective cells. This mechanism is not a turbulent diffusion, cannot occur in collisionless systems, and is the analog of the well-known laminar “magnetic flux expulsion” in magnetohydrodynamics. This expulsion process involves a “pinch” across closed streamlines and further results in the formation of pressure fingers along the separatrix of the convective cells. By nature, these coherent structures are dissipative because the mixing process that leads to their formation relies on a finite amount of collisional diffusion. Numerical simulations of two-dimensional interchange modes confirm the role of laminar expulsion by convective cells for profile consistency and structure formation. They also show that the fingerlike pressure structures ultimately control the rate of heat transport across the plasma layer and thus the transport scaling at large Rayleigh numbers. This contradicts mixing-length arguments which do not account for collisional processes. For interchange modes, the problem of coherent structure formation, profile consistency, and transport scaling are thus intimately linked.