Chemical transport by weakly nonlinear internal gravity waves

Internal gravity waves are known to transport chemicals and other tracers in many geophysical and astrophysical systems. This study explores the potential role of internal gravity waves (IGWs) in facilitating chemical mixing within the radiative zones of stars using theoretical analysis and simulations, examining the behavior of IGWs under the Boussinesq approximation in a stratified flow. Low-amplitude gravity waves that do not break are considered. It is found that in the presence of radiative diffusivity, vertical transport occurs due to nonlinear interactions of IGWs with different wavevectors. The first-order transport by the nonlinear Eulerian mean cancels out with the Stokes drift. The next-order transport is obtained in terms of a diffusion equation using multiscale asymptotic analysis, achieving quantitative agreement with simulations. These results demonstrate that IGWs can induce substantial vertical chemical mixing with nonlinear interactions and radiative diffusivity being key factors, providing a reliable quantification of the transport process by IGWs.