Renormalization group method for Farley-Buneman fluctuations: basic results
Abstract. Sudan and Keskinen 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 E x 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 (fk fk) k. The effect of the small scales on the large scale dynamics in the limit k -> 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 Hamza and Sudan [1995], but one can also extract the skewness of the spectra as we do in this paper.
