Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration

Context. Stellar interiors are the seat of effcient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the di erential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal di usivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component ˜ f and the vertical component f . Methods.We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f -plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Je reys (WKBJ) approximation for nondi usive and highly-di usive fluids. Results. As in the traditional f -plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as ˜ f increases and its maximum growth rate increases significantly, while the thermal di usivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly a ected; for instance, the inertially unstable regime is also extended in the nondi usive limit as 0 < f < 1 + ˜ f 2=N2, where N is the dimensionless Brunt- Väisälä frequency. More strikingly, in the high thermal di usivity limit, it is always inertially unstable at any colatitude except at the poles (i.e., 0 < < 180). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical esults, we propose a prescription for the e ective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is effcient to redistribute angular momentum and to mix chemicals in stellar radiation zones.