Downflow plumes and entropy balance in deep convection zones

Computer Science – Numerical Analysis

Scientific paper

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Atmospheric Models, Balance, Entropy, Solar Convection (Astronomy), Solar Flares, Solar Granulation, Compressible Flow, Computerized Simulation, Hydrodynamic Equations, Numerical Analysis, Three Dimensional Flow

Scientific paper

Numerical simulations of three-dimensional compressible convection have regularly exhibited a flow structure comprised of narrow downflow plumes extending from the top to the bottom of the convection zone separated by regions of upwelling fluid vertically correlated over roughly a pressure scale height. The entropy generated through viscous dissipation of the flow is constrained by the difference of entropy flux through the boundaries and, to a lesser extent, the entropy generated by radiative diffusion. This constraint is used to derive a relation between the downflow plume number, width, and velocity as a function of reference atmosphere parameters for several model convection zones. In the case of the solar convection zone the assumptions of constant plume width, constant downflow plume velocity, and an upflow velocity with a mixing length depth dependence require that the downflow velocity be in the range 0.9 to 0.4 km/sec for plume widths in the range 1 to 10 Mm if the plume number at the bottom of the supergranules is equal to the number of the supergranules. At the bottom of the convection zone the plum number will be decreased by a factor of roughly 10. In the realm of numerical simulations, it is proposed that solutions be generated in a new non-barotropic reference atmosphere having a variable superadiabatic gradient chosen to hinder the formation of sharp viscous boundary layers. Plume number formulae are derived with the new reference atmosphere for both the laminar and strong turbulence regimes.

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