Chemical transport by weakly nonlinear internal gravity waves in stars

While it is well-known that internal gravity waves (IGWs) transport chemicals in the radiative zones of stars, there remains substantial uncertainty on the amount of, and physical mechanism behind, this transport. Most previous studies have relied on heuristic theories, or numerical simulations that may be hard to extrapolate to stellar parameters. In this work, we present the first rigorous asymptotic calculation of (passive) chemical transport by IGWs, in the limit of small wave amplitude. We find that the net transport by a coherent packet of waves scales like wave amplitude to the fourth power, and verify these analytic calculations with numerical simulations. Because the transport is equally likely to be positive as negative, the transport by a random superposition of waves is expected to scale as wave amplitude to the eighth power. These results show that closer comparisons between theoretical arguments and numerical calculations are essential for interpreting numerical simulations of chemical transport by IGWs, and making accurate predictions of this process for stellar evolution modeling.