Dynamics of Mixed Convective--Stably-Stratified Fluids

We study the dynamical regimes of a density-stratified fluid confined between isothermal no-slip top and bottom boundaries (at temperatures $T_t$ 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 $T_b>T_i>T_t$. 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 Rayleigh-Benard 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 quantities for different stratification strengths. 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.