Four dynamical regimes for a starting plume model

Abstract

The growth of two-dimensional plumes was modeled numerically to study the dynamics of plumes with Rayleigh numbers in the range of 104 to 108 and Prandtl numbers in the range of 0.025 to 10 000. In this study we deal with a geometry driven by a heated line source, which is different from the basally heated Rayleigh–Bénard convection between two horizontal plates. We found four different regimes for plume growth: a diffusive-viscous regime characterized by both thick thermal and velocity boundary layers; an inviscid-diffusive regime with thin velocity and thick temperature boundary layers; a viscous nondiffusive regime with thick velocity boundary layers and thin thermal ones; and an inviscid nondiffusive regime with both thin velocity and narrow thermal boundary layers. We also studied the dependence of the Nusselt number on height for various Rayleigh and Prandtl numbers. We found that plumes with Prandtl numbers as high as 104 grown at a high Rayleigh number (108) are significantly different from plumes developed in an infinite Prandtl number fluid.