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

Abstract

Stellar radiation zones play a key role in the long-term magneto-rotational and chemical evolution of stars. As parts of the oceans and of the atmosphere of the Earth, their dynamics is controlled by the Archimedean buoyancy force and the Coriolis acceleration. They are the seat of an efficient extraction of angular momentum and of a mild mixing of chemicals. In this context, particle tracing in recent nonlinear hydrodynamical equatorial numerical simulations of stellar radiation zones where internal gravity waves (hereafter IGWs) are propagating 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 are not fullfiled. This effective diffusivity is found to scale as the squared velocity of IGWs for every rotation rates. Other dependences have also been derived in the literature, for instance in the case of the Stokes displacement. To interpret these results, we propose to explore the parameterisation for the mixing of particles, which has been proposed for the oceans. 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 demonstrate that this diffusivity 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 characterize 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, which triggers mixing, for any rotation rate.

5 pages, 1 figure, Accepted for publication as a Letter in Astronomy \& Astrophysics

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