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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 3, issue 1
Nonlin. Processes Geophys., 3, 41–46, 1996
https://doi.org/10.5194/npg-3-41-1996
© Author(s) 1996. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: URSI and STEP/GAPS Workshop

Nonlin. Processes Geophys., 3, 41–46, 1996
https://doi.org/10.5194/npg-3-41-1996
© Author(s) 1996. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Mar 1996

31 Mar 1996

Renormalization group method for Farley-Buneman fluctuations: basic results

A. M. Hamza A. M. Hamza
  • Physics Department, Center for Space Research, University of New Brunswick, Fredericton, NB E3B 5A3, Canada

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.

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