Study of two-dimensional interchange turbulence

An eddy viscosity model describing enstrophy transfer in 2D turbulence is presented. This model provides an equation for the energy spectral function F(k) as a function of the energy input rate to the system per unit wavenumber, gamma(sub s)(k). In the enstrophy-transfer inertial range, F(k) varies as k(exp -3) is predicted by the model. The eddy viscosity model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation of the 2D interchange turbulence demonstrates that the energy spectrum in the high wavenumber region 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 Prandtl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for gamma(sub s)(k), our theoretical model predicts that Nu varies as (Ra . Pr)(exp 1/2) for a constant background pressure gradient and Nu varies as (Ra . Pr)(exp 1/3) for a self-consistent background pressure profile with the stress-free slip boundary conditions. The latter agrees with our numerical result showing Nu varies as Ra(exp 1/3).