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The Influence of Boundaries on the Stability of Compositional Plumes

Khaled S. Al-Mashrafi, Ibrahim A. Eltayeb
2014 Open Journal of Fluid Dynamics  
The influence of boundaries on the dynamics of a compositional plume is studied using a simple model in which a column of buoyant fluid rises in a less buoyant fluid bounded by two vertical walls with a finite distance apart. The problem is governed by four dimensionless parameters: The Grashoff number, R, which is a measure of the difference in concentration of light material of the plume to its surrounding fluid, the Prandtl number, σ, which is the ratio of viscosity, ν, to thermal
more » ... thermal diffusivity, κ, the thickness of the plume, 2x 0 , and the distance, d, between the two vertical walls relative to the salt-finger length scale. The influence of the boundary on the fluxes of material, heat, and buoyancy is examined to find that the buoyancy flux possesses a local maximum for moderate to small thicknesses of the plume when they lie close to the wall. This has the effect of introducing a region of instability for thin plumes near the wall with an asymptotically larger growth rate. In addition, the presence of the boundary suppresses the three-dimensional instabilities present in the unbounded domain and allows only two-dimensional instabilities for moderate to small distances between the bounding walls.
doi:10.4236/ojfd.2014.41007 fatcat:y5zqiqff7zaypasw2dyayf23nu