Geophysical research: article

E. Dmitriev
Borok Geophysical Observatory of Schmidt Institute of Physics of the Earth of the Russian Academy of Science
Journal: Geophysical research
Tome: 21
Number: 1
Year: 2020
Pages: 50-60
UDK: 551.594
DOI: 10.21455/gr2020.1-4
Full text
Keywords: atmospheric electricity, mathematical modeling, electrode effect
Аnnotation: The electrical condition of weak ionized surface atmosphere is formed by the electrode effect resulting in dependence of electric characteristics on distance to an electrode (underlying surface) because of the repulsion of the similarly charged air ions. Mathematically the surface electrode effect is described by a differential boundary problem for electric field and concentration of positive and negative air ions as altitude functions, with a boundary condition of equality to zero of negative air ions concentration on the underlying surface. Far away from the underlying surface an equality between unknown air electrical quantities and their equilibrium values is desired. Under the turbulent electrode effect, air ions are transported not only by electric forces, but also by turbulent diffusion. It leads to absorption of all air ions by an underlying surface and to an additional boundary condition. Usually boundary conditions are given at surface roughness parameter altitude, due to the fact that turbulent diffusion below it is absent. In this paper the surface turbulent electrode effect is considered in the assumption that the coefficient of turbulent diffusion increases with altitude under the power law above the surface roughness parameter altitude, and molecular diffusion takes place below it. At the same time densities of air ion flows are continuous at the surface roughness parameter altitude. The examples of numerical solutions of the corresponding boundary problem for the typical scales representative for the surface atmosphere of middle latitudes are presented. The solutions are compared with the solutions of a problem in traditional definition where the area below a surface roughness parameter is not considered, and boundary conditions are desired at the altitude of surface roughness parameter. It is shown that the magnitudes of the electrode effect are rather close in both problem definitions, at the same time altitude profiles of concentrations of air ions in the area above a surface roughness parameter obtained from the considered problem solution differ from the altitude profiles obtained from the solution of the problem in traditional definition.