Study of Two-Dimensional Interchange Turbulence

Abstract

An eddy viscosity model describing enstrophy transfer in two-dimensional turbulence is presented. It is similar to that of Canuto et al . [Phys. Fluids 30 (1987) 3391] and provides an equation for the energy spectral function F ( k ) as a function of the energy input rate per unit wavenumber, γ s ( k ). In the enstrophy-transfer inertial range, F ( k )∝ k -3 is predicted by the model. Our model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation demonstrates that the energy spectrum for high wavenumbers is well described by this model. The turbulent transport driven by the interchange turbulence is expressed in terms of the Nusselt number Nu, the Rayleigh number Ra and the Prantl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for γ s ( k ), our theoretical model predicts that Nu∝(Ra·Pr) 1/2 for a constant background pressure gradient and Nu∝(Ra·Pr) 1/3 for a self-consistent background pressure profil...