Numerical Model of the Return Stroke of the Lightning Discharge

The numerical model of a spark discharge in air, described in the preceding paper [Phys. Fluids 14, 2111 (1971)], is used to compute the properties of the discharge channel of a lightning return stroke and its acoustic wave. Initial conditions and electric current waveforms were varied over a wide range, to correspond with the observed variability of natural lightning events. Computed temperatures, pressures, and electron densities in the discharge channel agree well with available observational data. The model predicts temperatures near the upper limit of the range of spectroscopically determined temperatures. Discharge channel radii agree well with similarity solutions for the growth of a spark channel. The energy dissipated per unit length of the discharge channel and the strength of the pressure wave lie well below most literature estimates. The computed energy inputs fall between 10 and 60 J/cm, and depend primarily on the maximum values of the discharge current.