Supergranule aggregation for constant heat flux-driven turbulent convection

Abstract

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

arXiv comment15 pages, 11 figures

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Cited by in corpus (14)

• Combined particle image velocimetry and thermometry of turbulent superstructures in thermal convection
• Convective mesoscale turbulence at very low Prandtl numbers
• Thermal boundary condition studies in large aspect ratio Rayleigh-Bénard convection
• Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection
• Lagrangian heat transport in turbulent three-dimensional convection
• Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows
• Spatially resolved spectroscopy across stellar surfaces. IV. F, G, & K-stars: Synthetic 3D spectra at hyper-high resolution
• Turbulent mesoscale convection in the Boussinesq limit and beyond
• Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection
• Digital twin of a large-aspect-ratio Rayleigh-Bénard experiment: Role of thermal boundary conditions, measurement errors and uncertainties
• Supergranule aggregation: a Prandtl number-independent feature of constant heat flux-driven convection flows
• Effects of conjugate heat transfer on large-scale flow structures in convection
• Three-dimensional velocity gradient statistics in a mesoscale convection laboratory experiment
• Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection