Analytical Investigation of the Reaction‐Diffusion Waves in the Mesopause Photochemistry

Abstract

The mechanism of the generation of reaction-diffusion waves in the mesopause region (80-90 km) has been studied analytically. These waves are the propagating phase fronts arising in the oscillations of O, O 3 , H, OH, and HO 2 concentrations. They appear in the presence of horizontal eddy diffusion in zonal direction when mesospheric photochemistry responds subharmonically (with a period of 2 days) to diurnal variations of solar radiation. The photochemical system in the mesopause region is a nonlinear oscillator which can be roughly described by a system of two differential nonautonomous equations with power law nonlinearity which was derived in our earlier papers. To model the wave propagation, we have considered a continuous chain of oscillators with diffusion coupling and with the phase of external periodic forcing depending linearly on spatial coordinates. It was found that the reaction-diffusion waves are caused by specific "wind" type transport appearing in the equations for the amplitudes of 2-day photochemical oscillations of O and H concentrations due to the zonal inhomogeneity of the external forcing. The obtained expression for the wave propagation velocity fully confirmed the earlier numerical results that the magnitude of the velocity is proportional to the diffusion coefficient and the gradient of the external forcing phase. The wave propagation direction is determined by the definite phase relations specified by internal parameters of the system only.

The 2‐Day Photochemical Oscillations in the Mesopause Region: The First Experimental Evidence?

“…One At the heights of the nonlinear response region (see Figures 1d and 1g), 2DPO are much more pronounced in the H behavior. In the O evolution, the amplitude of «true» oscillations with a period of 2 days is remarkably smaller than the amplitude of diurnal oscillations (Kulikov et al, 2020 Konovalov and Feigin (2000), the nonlinear response (and, hence, 2DPO) is produced by a nontrivial structure of the system phase space at nighttime: there are two different areas with low and high speed of the variable's change. If the system arrives in the region with low speed at sunset, it evolves further in the regime of "high night H," and vice versa.…”

“…At the heights of the nonlinear response region (see Figures 1d and 1g), 2DPO are much more pronounced in the H behavior. In the O evolution, the amplitude of «true» oscillations with a period of 2 days is remarkably smaller than the amplitude of diurnal oscillations (Kulikov et al., 2020). Let us analyze the evolution of the variables at 85 km at successive nights.…”

“…These waves were studied analytically by Kulikov et al. (2020). With the use of 1‐D and two‐dimensional (2‐D) models, Kulikov (2004, 2007) investigated the influence of a quasi‐2‐day atmospheric wave on the 2DPO and revealed the possibility of spatial synchronization between the wave and the 2DPO phase distribution.…”

“…With the use of 1-D model, Feigin (2004, 2005) showed that the eddy diffusion in zonal direction leads to the appearance of a new (for nonlinear dynamics) type of reaction-diffusion waves in the form of propagating phase fronts of 2DPO. These waves were studied analytically by Kulikov et al (2020). With the use of 1-D and two-dimensional (2-D) models, Kulikov (2004Kulikov ( , 2007 investigated the influence of a quasi-2-day atmospheric wave on the 2DPO and revealed the possibility of spatial synchronization between the wave and the 2DPO phase distribution.…”