Autowave Regimes of Thundercloud Electrification

We consider the evolution of the electric field and charge in a one-dimensional electrohydrodynamic (EHD) distributed-parameter system which serves as a simple model of a thundercloud. A diffusion equation for the electric field is proposed which, under reasonable assumptions on the nonlinear dependence of the dissipation current on the electric field (caused by the corona effect around aerosol particles in strong fields), has autowave solutions describing the dynamics of spatially separated electric-charge regions in the thundercloud. The nonlinear set of equations describing the electric-field dynamics in an ensemble of colliding aerosol particles and light ions is reduced to a rather simple basic model which admits solutions in the form of traveling fronts and traveling pulses. We find the asymptotic values of the velocity and thickness of the space-charge front, which are determined by the diffusion and the separation and conductivity currents. Using these values, we estimate the electrostatic-energy growth rate in a thunderstorm cell at the stage of its intensive electrification. A possibility is shown of the formation of a traveling pulse of field and conductivity in such an EHD system with allowance for inductive and noninductive mechanisms of aerosol-particle charging.