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<i>Sudan and</i> <I>Keskinen </I>in [1979] derived a set of equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the <B>E x B</B> or gradient-drift instability. This problem is of fundamental importance in ionospheric physics. The nonlinear nature of the equations makes it very hard to write a closed form solution. In this paper we propose to use "Dynamical Renormalization Group" methods to study the long-- wavelength, long-time behaviour of density correlations generated in this ionospheric plasma stirred by a Gaussian random force characterized by a correlation function (f<em><B><sub>k </sub></B></em>f<em><B><sub>k</sub></B></em>) <b><i>k</i></b>. The effect of the small scales on the large scale dynamics in the limit <i><b> k</b></i> -> 0 and infinite "Reynolds" 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, then one can not only derive a subgrid model based on the results of RNG, and this has been done by <I>Hamza and Sudan</I> [1995], but one can also extract the skewness of the spectra as we do in this paper.