Steady Convection in Deep Compressible Layers

Abstract

The standard mixing-length model of convection traditionally used in astrophysics is based on an anology with the kinetic theory of gases; convective eddies travelling a distance ℓ before mixing with the background. The mixing length ℓ is assummed to be of the order of the local scale height of density or pressure, on the grounds that if, at any one level, upward moving material occupies half the area, then on travelling a scale height it would have expanded to fill all the available area (cf Biermann (1935). Simulations of steady convection do not find eddies to be of the order of the local scale height, but rather a single cell extending over several scale heights from top to bottom of the layer (cf Graham 1975, Chan and Wolf 1982, Hulburt et al 1994, Roxburgh and Simmons 1993). Simulations of turbulent convection with some form of sub-grid scale closure give plumes or downdrafts extending over several scale heights (cf Nordlund and Stein 1996, Singh, Roxburgh and Chan 1995). We here present a simple explanation of these results.