Chemical transport by weakly nonlinear internal gravity waves in stars

While internal gravity waves (IGWs) are known to transport chemicals in the radiative zones of stars, substantial uncertainty remains regarding the magnitude and physical mechanisms of this transport. Most previous studies have relied on heuristic theories or numerical simulations that are difficult 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. The net vertical transport induced by a coherent packet of waves is found to be proportional to the horizontal mean of (w S+w E) squared, where w S and w E are the vertical Stokes and Eulerian mean velocities. The transport scales as the fourth power of wave amplitude and quadratically with time, and we verify these scalings with numerical simulations. In the weakly damped regime, the dominant transport coefficients scale as ω-2κ squared, where ω is the wave frequency and κ is the radiative diffusivity. Because the transport can be positive or negative depending on the wave phases, the effective mixing induced by the superposition of coherent wave packets is expected to scale with the eighth power of wave amplitude. These results provide a theoretical foundation for making accurate predictions of IGW-induced chemical transport in stellar evolution models.