Modeling Fractal Dynamics of “Warm” Thunderstorms Electrical Parameters with Various Electrification Components

This paper proposes a universal mathematical model for describing a charged particle and electric field strength dynamics near hydrometeors and charged drops surfaces in clouds. A thundercloud containing hydrometeors and drops is chosen as the object for study, since it can have a significant impact on the weather conditions and climate of the Earth. Using the fractional integro-differentiation we obtain analytical solution to the model equation, in which the fractal structure is taken into account through a phenomenological parameter that determines the intensity of the charge and the electric field in the vicinity of the charged cloud particles. The role of solid hydrometeors and drops in a thundercloud electrodynamics (formation, accumulation, separation of electric charges) including the cloud fractal property is analyzed. Calculations have shown that the electric field is capable to pull up dipoles of polarized water molecules and ions with the opposite sign to the hydrometeor and drops. Transition zones of charge and electric field strength dynamics near the charged spherical surfaces are found for variable fractal dimension which depend on the particle initial parameters.