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Localized electrical current propagation in anisotropically perturbed atmospheres
Author(s) -
Zohdi T. I.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2881
Subject(s) - isotropy , anisotropy , microscale chemistry , electrical conductor , mechanics , physics , perturbation (astronomy) , electrical resistivity and conductivity , wavefront , computational physics , classical mechanics , optics , mathematics , quantum mechanics , mathematics education
The trajectory of free atmospheric electrical currents, such as lightning and sparks, is strongly influenced by microscale events that occur at the current front. In particular, highly conductive pathways can occur at the free surface front due to dielectric breakdown . The specific directions of the local pathways are minutely perturbed, due to the gaseous, disordered, nature of the media at the small scale. This results in highly conductive, anisotropically perturbed, continuum‐level properties at the electrical current front. In this work, a model is developed to investigate the role of the resulting anisotropically perturbed conductivity at the propagation front on the overall trajectory of free atmospheric electrical currents. The approach is to relate the electrical current velocity to the local anisotropic conductivity at the propagation front and the surrounding electric field. The conductive anisotropy is decomposed into an isotropic ‘base state’ and an anisotropic perturbation. The current trajectory is shown to be governed by a set of non‐linear differential equations, for which a numerical solution scheme is developed. The difference between paths taken through anisotropically perturbed and isotropic media is analytically bounded and quantified numerically as a function of the magnitude of the anisotropic perturbation. The analysis and numerical experiments indicate that, in a statistical sense, the difference in the paths taken in anisotropically perturbed and isotropic media depends quasilinearly on the perturbation magnitude. Copyright © 2010 John Wiley & Sons, Ltd.