SUBGRID MODELING OF CONVECTIVE TURBULENCE IN WEAKLY IONIZED COLLISIONAL PLASMA BY RENORMALIZATION-GROUP ANALYSIS

The equations governing the nonlinear evolution of density fluctuation s in a low-pressure weakly ionized plasma driven unstable by the E x B or gradient-drift instability were derived by Sudan and Keskinen (197 7, 1979) for addressing the electrostatic turbulence in the E and F re gions of the Earth's ionosphere. We have developed a subgrid model sui table for the numerical simulation of these equations which is closely related to renormalized diffusion caused by small-scale fluctuation s pectrum. ''Dynamical Renormalization Group'' (RNG) methods are employe d to obtain the renormalized diffusion. This procedure computes the lo ng-wavelength, long-time behavior of density correlations generated by the evolution equation for the plasma stirred by a Gaussian random fo rce characterized by a correlation function proportional to k(m) where k is the wavenumber of the forcing function. The effect of small scal es on the large-scale dynamics in the limit k --> 0 and infinite Reyno lds number can be expressed in the form of renormalized coefficients; in our case, renormalized diffusion. If one assumes the power spectra to be given by the Kolmogorov argument of cascading of energy through k space then one can derive a subgrid model based on the results of RN G.