Convective Cooling of Lightning Channels

Abstract
We report experimental data which trace the time development of electric discharge channels in air and which demonstrate the turbulent cooling of such channels. These data provide qualitative confirmation of the model proposed and used by Hill, Rinker and Wilson to calculate the production of nitrogen oxides by lightning. We outline an analytical treatment which identifies asymmetries in the pressure and density gradients of the discharge channel as a significant source of vorticity. The vorticity, in turn, causes ambient air to mix into the channel. Our theoretical analysis results in equations from which the vorticity strength and mixing time scale may be calculated. We briefly describe detailed simulations with which we have calibrated the theory. Finally, we combine the experimental data with our calibrated formulas to estimate the convective mixing rate in the case of lightning. We obtain a rate of ∼400 s−1 for the return stroke channel after pressure equilibrium has been achieved. Abstract We report experimental data which trace the time development of electric discharge channels in air and which demonstrate the turbulent cooling of such channels. These data provide qualitative confirmation of the model proposed and used by Hill, Rinker and Wilson to calculate the production of nitrogen oxides by lightning. We outline an analytical treatment which identifies asymmetries in the pressure and density gradients of the discharge channel as a significant source of vorticity. The vorticity, in turn, causes ambient air to mix into the channel. Our theoretical analysis results in equations from which the vorticity strength and mixing time scale may be calculated. We briefly describe detailed simulations with which we have calibrated the theory. Finally, we combine the experimental data with our calibrated formulas to estimate the convective mixing rate in the case of lightning. We obtain a rate of ∼400 s−1 for the return stroke channel after pressure equilibrium has been achieved.