Convection driven by temperature and composition flux with the same diffusivity
Whitehead, John A.
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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.
Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Geophysical & Astrophysical Fluid Dynamics 111 (2017): 229-248, doi:10.1080/03091929.2017.1333608.
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