Convection driven by temperature and composition flux with the same diffusivity

Abstract

Temperature, pressure, and composition determine density of fluids within the earth, the ocean, our atmosphere, stars and planets. In some cases, variation of composition component C competes equally with temperature T to determine buoyancy-driven flow. Properties of two-dimensional cellular convection are calculated with density difference between top and bottom boundaries determined by difference of temperature T (Dirichlet boundary conditions, quantified by Rayleigh number Ra that is positive destabilising), fluxes of C (Neumann boundary conditions quantified by Raf that is positive stabilising), and Prandtl number Pr. Numerical solutions in a 2-dimensional rectangular chamber are analysed for Prandtl numbers Pr=1,∞. For Ra and Raf>0 and Raf above approximately 300, subcritical instability separates T-driven convection from C-dominated stagnation. The flow is steady but a sudden change in Ra or Raf produces decaying pulsations to the new flow. A boundary layer solution for rapid flow exists in which T, which has the Dirichlet condition, is more sensitive to flow speed than C with the Neumann condition. A new type of pulsating flow occurs for Ra and Raf<0. The pulsations are characterised by slow flow with gradually strengthening compositional plumes in a thermally stratified flow interrupted by rapid flow with gradually weakening compositional plumes. In this slow speed range, C is more sensitive to speed than T.