Investigations of wave-induced nonlinear response of minor species with the KBM averaging method

An analytical solution to the continuity equation of minor species was for a long time obtained only with a linear treatment owing to the fact that secularity would arise when a direct perturbation expansion was applied to the equation. Recently, Huang et al. (2003) applied the Krylov-Bogoliubov-Mitropolsky (KBM) averaging method to remove the higher-order secular terms in the perturbation expansion series, and what remained in the series were the terms that oscillate at frequencies that are an integer multiple of the forcing wave frequency. A vertical drift velocity demonstrated to be the Eulerian drift was required to remove the secular terms. Following the previous work, a coupled chemical-dynamical gravity wave model with the application of the KBM method is presented here to investigate the wave-induced nonlinear response. The significance of the higher-order nonlinear response will be investigated. Results indicate that higher-order terms are significant when the scale height of the minor species is small.