TITLE:
The Influence of Boundaries on the Stability of Compositional Plumes
AUTHORS:
Khaled S. Al-Mashrafi, Ibrahim A. Eltayeb
KEYWORDS:
Compositional Plumes; Flux; Stability; Growth Rate; Bounded Domain
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.4 No.1,
March
24,
2014
ABSTRACT: 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 diffusivity, κ, 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.