Understanding hydrodynamical wave-driven shear mixing in stellar radiation zones. Looking in the mirror of the dyapicnal oceanic mixing

Stellar radiation zones play a key role in the long-term magneto-rotational and chemical evolution of stars and of their planetary and galactic neighborhoods. Similarly to parts of the atmosphere and oceans of the Earth, they are stably stratified and rotating. Therefore, their dynamics is controlled by the Archimedean buoyancy force and the Coriolis acceleration. Asteroseismology and high-resolution spectroscopy have showed that they are the seat of an efficient extraction of angular momentum and of a mild mixing of chemicals that must be more fully understood. In this context, particle tracing in recent non-linear hydrodynamical equatorial numerical simulations of stellar radiation zones, where internal gravity waves (IGWs) are propagating, has led to the measurement of an effective diffusivity following the prescriptions derived by Garcia-Lopez & Spruit and by Zahn for the inflectional instability of the vertical shear of low-frequency IGWs. However, the associated instability criteria have not been fulfilled. This effective diffusivity is found to scale as the squared velocity of IGWs for every rotation rates. Other dependencies have also been derived in the literature as, for instance, in the case of the Stokes displacement. We aim to provide a physical interpretation of these phenomena. To reach this objective, we propose exploring the parameterisation for the mixing of particles, which has been proposed in another rotating stably stratified systems: the oceans of Earth. A foundation stone in physical oceanography is the so-called Osborn & Cox energetic balance that leads to an effective dyapicnal diffusivity for the transport of matter that scales as the ratio of the dissipation of the fluctuating flows over the squared Brunt-Väisälä stratification frequency. We applied this parameterisation for the mixing to the field of low-frequency IGWs propagating in stellar radiation zones. We demonstrate that the effective dyapicnal diffusivity, widely used in modeling the oceanic general circulation, is equivalent to the eddy diffusivity derived by Zahn for the inflectional instability of the vertical shear applied to low-frequency IGWs. This allows us to characterise the corresponding energetic balance where the power extracted by the waves from the mean flows is balanced by their dissipation and by the power produced by their buoyancy flux for any rotation rate. This bridge established between results obtained across geophysical and stellar fluid dynamics illustrates the high interest of a cross-fertilisation between these research fields when we are aiming to evaluate and robustly model the effects of small-scale and short-timescale phenomena such as IGWs on the long-term evolution of large-scale oceanic, atmospheric, and stellar general circulation processes.