On nonlinear response of minor species with a layered structure to gravity waves

We investigate the temporal and spatial variations of the local and integrated response of minor species and OH emission to a small-scale gravity wave. A Chapman-like function is used to model the unperturbed profiles of minor species like ozone, hydrogen, and OH emission. Because the gravity waves that we simulate do not violate the nonacceleration conditions, the waves will not cause a secular variation in the minor species concentrations. We therefore use the Krylov-Bogoliubov-Mitropolsky averaging method to remove the higher-order secular terms in our perturbation expansion. A vertical drift velocity, second order in nature, is required to remove the secular terms. The equivalence of this vertical drift velocity to the Eulerian drift is demonstrated. Using the perturbation method to treat the response of minor species to a small-scale gravity wave, we compute the first- and second-order perturbation terms and find that the second-order terms will also be important for narrow minor species profiles having large gradients (or Small-Scale heights).