%0 Journal Article
%T The Influence of Boundaries on the Stability of Compositional Plumes
%A Khaled S. Al-Mashrafi
%A Ibrahim A. Eltayeb
%J Open Journal of Fluid Dynamics
%P 83-102
%@ 2165-3860
%D 2014
%I Scientific Research Publishing
%R 10.4236/ojfd.2014.41007
%X 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, ¦Ò, which is the ratio of viscosity, ¦Í, to thermal diffusivity, ¦Ê, the thickness of the plume, 2x0, 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.
%K Compositional Plumes
%K Flux
%K Stability
%K Growth Rate
%K Bounded Domain
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=44088