Chapman's model for ozone concentration: earth`s slowing rotation effect in the atmospheric past

Abstract

Chapman's model for ozone concentration is studied. In this nonlinear model, the photodissociation coefficients for $O_{2}$ and $O_{3}$ are time-depending due to earth-rotation. From the Kapitsa's method, valid in the high frequency limit, we find the criterion for the existence of equilibrium solutions. These solutions are depending on the frequency, and require a rotation period $T$ which satisfies $T<T_{1}$ or $T>T_{2}$. Where the critical periods $T_{1}$ and $T_{2}$, with $T_{2}>T_{1}$, are a function of the parameters of the system (reaction rates and photodissociation coefficients). Conjectures respect to the retardation of the earth's rotation, due to friction, suggest that the criterion was not even verified in the atmospheric past.