Nonlinear Gravity-Wave Effects on the Distribution of Chemical Constituents in a Vertically-Sheared Atmospheric Flow

The dynamical processes in the atmosphere are coupled with the chemistry of the atmosphere. Internal gravity waves influence the distribution of chemical constituents in the atmosphere through their effects on the background wind or mean flow. We examine a coupled system of equations comprising a nonlinear transport equation of Fisher type for the distribution of the chemical species, along with nonlinear Boussinesq equations for internal gravity waves in a vertically stratified and vertically sheared fluid flow in a two-dimensional region. In our model, a horizontally localized gravity-wave packet is generated and propagates upward into a localized region where the chemical species is present. Numerical solutions show that the wave-induced mean flow resulting from nonlinear gravity-wave interactions in the vicinity of a critical level leads to modifications in the distribution of the chemical. An asymptotic analysis of a related qualitatively similar problem gives us information on the dominant behaviour of the chemical concentration perturbation. We conclude that nonlinearity and vertical shear play a vital role in the interplay between gravity-wave dynamics and chemical distributions in the atmosphere.