Supergranule aggregation for constant heat flux-driven turbulent convection

Turbulent convection processes in nature are often found to be organized a hierarchy of plume structures and flow patterns. The gradual aggregation cells or granules supergranule which eventually fills the whole horizontal layer is reported analysed spectral element direct numerical simulations three-dimensional turbulent Rayleigh-B\'{e}nard at an aspect ratio $60$. formation proceeds over time span more than $10^4$ convective units for largest accessible Rayleigh number occurs only when turbulence driven by constant heat flux imposed bottom top planes enclosing layer. resulting inverse cascade process observed both temperature variance kinetic energy. An additional analysis leading Lyapunov vector field full trajectory its high-dimensional phase space demonstrates that modes certain scale continue give rise locally with longer wavelength case. As consequence successively larger patterns grow until extension reached. This instability mechanism, known exist near onset flux-driven convection, shown here persist into fully developed regime thus connecting weakly nonlinear pattern one turbulence. We discuss possible implications our study observed, but not yet consistently numerically reproducible, solar supergranulation could lead improved simulation models surface Sun.