Modeling stellar convective transport with plumes : II. Transport Properties of Locally and Non-locally driven Convection

TL;DR

The paper investigates how plume-driven cooling in stellar convection alters energy transport compared with entropy-gradient-driven convection. Using 3D DNS, it shows that standard gradient-diffusion closures fail in the cooling-driven regime due to intermittent, coherent plumes near the surface, which produce non-Gaussian statistics and a markedly enhanced turbulent flux. By isolating coherent plume motions with Time-Space Double Averaging (TSDA) and embedding their influence into a non-equilibrium diffusivity, the authors achieve quantitative agreement with simulations, linking plume dynamics to mean-field transport via a calibrated closure with $ ilde{\boldsymbol{u}}$-dependent corrections. This work provides a physically transparent framework for improving subgrid models of non-equilibrium stellar convection zones and outlines pathways for incorporating rotation, magnetic fields, and radiative transfer in future studies.

Abstract

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.

Figures (12)

• Figure 1: Schematic illustrations of (a) the cooling-driven convection model (Model C) and (b) the entropy-gradient–driven convection model (Model S). Panel (c) shows a 3D visualization of the numerical setup adopted in this study and the typical convective state realized in our simulations (vertical velocity $u_z$ in Model C is shown as a reference).
• Figure 2: Temporal evolution of volume-averaged kinetic energy, $\epsilon_{\rm kin} = \langle \rho \delta \bm{u}^2/2\rangle_{\rm v}$, for Model C (blue solid) and Model S (red dashed), where $\delta \bm{u} \equiv \bm{u} - \langle \bm{u} \rangle_{\rm h}$.
• Figure 3: Distribution of $\delta S$ on the horizontal cutting plane at $z = 0.95$ (top) and the vertical cutting plane at $y=0$ (bottom) for (a) Model C and (b) Model S, where $\delta S \equiv S - \langle S \rangle_{\rm h}$ is the fluctuating component of the entropy. The brighter (darker) tone corresponds to the region with a higher (lower) entropy than its horizontal average.
• Figure 4: Spectrum of $\delta u_z^2$ for Model C (blue solid) and Model S (red dashed). The spectrum taken at each depth is projected onto a 1D wavenumber $k^2 = k_x^2 + k_y^2$ and then is averaged over the upper CZ, i.e., height from $z = 0.9$ to $0.95$. The pale colored line corresponds to the original spectrum, whereas the dark colored line represents the spectrum after the application of the Bezier smoothing.
• Figure 5: Probability density on a horizontal plane at $z=0.95$ for (a) horizontal velocity $\delta u_h$, (b) vertical velocity $\delta u_z$, and (c) kinetic helicity $\mathcal{H} \equiv \delta u_z \cdot \omega_z$. Results are shown for Model C (blue solid) and Model S (red dashed). While $\delta u_h$ exhibits similar Gaussian-like distributions in both models, clear differences appear in $\delta u_z$, reflecting broader wings in Model C due to intermittent plume-like downflows.