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ABSTRACT We performed 3D hydrodynamic simulations of the inner $$\approx 50{{\ \rm per\ cent}}$$ radial extent of a $$25\,\,\mathrm{\mathrm{M}_\odot }$$ star in the early phase of the main sequence and investigate core convection and internal gravity waves in the core-envelope boundary region. Simulations for different grid resolutions and driving luminosities establish scaling relations to constrain models of mixing for 1D applications. As in previous works, the turbulent mass entrainment rate extrapolated to nominal heating is unrealistically high ($$1.58\times 10^{-4}\,\,\mathrm{\mathrm{M}_\odot \, {\mathrm{yr}}^{-1}}$$), which is discussed in terms of the non-equilibrium response of the simulations to the initial stratification. We measure quantitatively the effect of mixing due to internal gravity waves excited by core convection interacting with the boundary in our simulations. The wave power spectral density as a function of frequency and wavelength agrees well with the GYRE eigenmode predictions based on the 1D spherically averaged radial profile. A diffusion coefficient profile that reproduces the spherically averaged abundance distribution evolution is determined for each simulation. Through a combination of eigenmode analysis and scaling relations it is shown that in the N2-peak region, mixing is due to internal gravity waves and follows the scaling relation DIGW-hydro ∝ L4/3 over a $$\gtrapprox 2\,\,\mathrm{\mathrm{dex}}$$ range of heating factors. Different extrapolations of the mixing efficiency down to nominal heating are discussed. If internal gravity wave mixing is due to thermally enhanced shear mixing, an upper limit is $$D_\mathrm{IGW}\lessapprox 2$$ to $$3\times 10^{4}\,\,\mathrm{cm^2\, s^{-1}}$$ at nominal heating in the N2-peak region above the convective core. 

ABSTRACT We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the ppmstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a $$1.2\, {\rm M}_{\odot }$$ upper RGB star. We perform simulations for different grid resolutions (7683, 15363, and 28803), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial set-up increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $$\sim 0.2\, H_P$$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.