Modeling stellar convective transport with plumes : II. Transport Properties of Locally and Non-locally driven Convection
We perform three-dimensional hydrodynamic simulations of two idealized regimes of stellar convection: a cooling-driven model (Model C) and an entropy-gradient-driven model (Model S). The two regimes exhibit striking contrasts: while Model S develops large, relatively stationary eddies excited at depth, Model C is dominated near the surface by intermittent plume-like downflows that produce broad non-Gaussian velocity distributions and a turbulent energy flux that exceeds Model S by nearly an order of magnitude in the upper convection zone. Conventional gradient-diffusion (GD) closures reproduce the transport in Model S but significantly underestimate it in Model C, demonstrating that plume-driven convection lies beyond the scope of local, gradient-based models. To address this, we introduce a Time-Space Double Averaging (TSDA) method that extracts coherent fluctuations, yielding a diagnostic variable $\tilde{\boldsymbol{u}}$ that peaks where the flux is largest. Building on this insight, we propose a modified GD closure in which the turbulent diffusivity is corrected by a plume-mediated term, achieving quantitative agreement with simulation results. Although the closure requires a calibrated model parameter and a careful choice of the averaging window, it provides a physically transparent framework that links coherent plume dynamics to mean-field transport, and offers a pathway toward improved subgrid models for non-equilibrium stellar convection zones.