The mechanism of non-linear photochemical oscillations in the mesopause region

Abstract

The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80–90 km) has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O₃, H, OH and HO₂ concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the period-doubling threshold permits separating explicitly a particular case of the Mathieu equation <i>ẍ</i> + &alpha; &middot; sin &omega; <i>t</i> &middot; <i>x</i> = 0, in which the first sub-harmonic (&omega;/2) of the exciting force starts to grow exponentially when the amplitude of external forcing (α) exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.