Formation of nitrogen oxides behind the shock front during explosions and electric spark discharges in the atmosphere

Based on Ya. B. Zel'dovich's kinetic model which describes nitrogen oxidation in heated air, we construct a generalized analytical theory for generation and “freezing” of thermal NO$_x$. The relations for determining the quantity of nitrogen oxides formed in intense shock waves of various symmetry have been found, and the yield of the thermal NO$_x$ in spherical shock waves excited by powerful explosions in air has been estimated. The pattern of NO$_x$ formation during natural spark discharge in the atmosphere has been constructed for the first time. For this purpose, using the laws of instantaneous cylindrical explosion we model the air cooling behind the shock wave excited by a linear spark discharge.