Abstract. We study the dynamical regimes of a density-stratified fluid confined between isothermal noslip top and bottom boundaries (at temperatures Tt and T b ) via direct numerical simulation. The thermal expansion coefficient of the fluid is temperature dependent and chosen such that the fluid density is maximum at the inversion temperature T b > T i > Tt. Thus, the lower layer of the fluid is convectively unstable while the upper layer is stably stratified. We show that the characteristics of the convection change significantly depending on the degree of stratification of the stable layer. For strong stable stratification, the convection zone coincides with the fraction of the fluid that is convectively unstable (i.e. where T > T i ), and convective motions consist of rising and sinking plumes of large density anomaly, as is the case in canonical RayleighBénard convection; internal gravity waves are generated by turbulent fluctuations in the convective layer and propagate in the upper layer. For weak stable stratification, we demonstrate that a large fraction of the stable fluid (i.e. with temperature T < T i ) is instead destabilized and entrained by buoyant plumes emitted from the bottom boundary. The convection thus mixes cold patches of low density-anomaly fluid with hot upward plumes, and the end result is that the T i isotherm sinks within the bottom boundary layer and that the convection is entrainment-dominated. We provide a phenomenological description of the transition between the regimes of plume-dominated and entrainment-dominated convection through analysis of the differences in the heat transfer mechanisms, kinetic energy density spectra, and probability density functions for different stratification strengths. Importantly, we find that the effect of the stable layer on the convection decreases only weakly with increasing stratification strength, meaning that the dynamics of the stable layer and convection should be studied self-consistently in a wide range of applications.

Bowman et al. (2019a) reported low-frequency photometric variability in 164 O-and B-type stars observed with K2 and TESS. They interpret these motions as internal gravity waves, which could be excited stochastically by convection in the cores of these stars. The detection of internal gravity waves in massive stars would help distinguish between massive stars with convective or radiative cores, determine core size, and would provide important constraints on massive star structure and evolution. In this work, we study the observational signature of internal gravity waves generated by core convection. We calculate the wave transfer function, which links the internal gravity wave amplitude at the base of the radiative zone to the surface luminosity variation. This transfer function varies by many orders of magnitude for frequencies 1 d −1 , and has regularly-spaced peaks near 1 d −1 due to standing modes. This is inconsistent with the observed spectra which have smooth "red noise" profiles, without the predicted regularly-spaced peaks. The wave transfer function is only meaningful if the waves stay predominatly linear. We next show that this is the case: low frequency traveling waves do not break unless their luminosity exceeds the radiative luminosity of the star; and, the observed luminosity fluctuations at high frequencies are so small that standing modes would be stable to nonlinear instability. These simple calculations suggest that the observed low-frequency photometric variability in massive stars is not due to internal gravity waves generated in the core of these stars. We finish with a discussion of (sub)surface convection, which produces low-frequency variability in low-mass stars, very similar to that observed in Bowman et al. (2019a) in higher mass stars.