Abstract
We report on three-dimensional convection structures in thermohaline stratification with the high Rayleigh number RaT = 7 ⋅ 107, the diffusion ratio δ = 0.01 and various initial density stability ratios R = 0.5, 0.8, and 1.1. According to the classification of buoyancy-driven instability in the parameter space (R, δ), the three cases are referred to follow the Rayleigh-Taylor (RT) mode, the mixed mode (MM) and the diffusive-layer convection (DCL) mode, respectively. Whether the shape of the peak is a finger under the RT mode or a spike under the MM/DLC mode, the 3D view of the interface is likely to be a rolling mountain with a doughnut-shaped vortex around the peak and a banded vortex above the ridge. The doughnut-shaped vortex is maintained around the peak if its growth continues under RT convection; otherwise, the vortex sheds off and moves upward from the peak under the DLC mode. Additionally, we have observed the previously unreported vortex stratification by the contact interface due to the differential diffusion effect.
Highlights
We report on three-dimensional convection structures in thermohaline stratification with the high Rayleigh number RaT = 7 · 107, the diffusion ratio δ = 0.01 and various initial density stability ratios R = 0.5, 0.8, and 1.1
For two miscible fluids in a porous medium or a Hele-Shaw cell, the flow dynamic follows Darcy’s law such that the base state density can be estimated using linear stability analysis, and the buoyancy-driven convection mode can be systematically classified in the (R, δ) parameter space based on the curve type of the one-dimensional base state density profile.[3,4,5]
This observation helped verify the numerical results in this study, and confirmed the assumption that the classification of the convection modes for stratification in the Hele-Shaw cell could be extended to the unbounded stratification that did not satisfy Darcy’s law.[9]
Summary
The buoyancy-driven instability influences the mass and heat transfer between two miscible fluids in many applications ranging from CO2 sequestration to soil contamination, stellar dynamics, chemical engineering, and oceanography.[1,2] For two miscible fluids in a porous medium or a Hele-Shaw cell, the flow dynamic follows Darcy’s law such that the base state density can be estimated using linear stability analysis, and the buoyancy-driven convection mode can be systematically classified in the (R, δ) parameter space based on the curve type of the one-dimensional base state density profile.[3,4,5] The upper solution contains a species A in concentration A0 with diffusion coefficient DA and solutal expansion coefficient α A, while the lower solution contains a solute B in concentration B0 with relative DB and αB. The 3D convection structures developed under different convection modes will be analyzed and compared
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