The Fluid Dynamics of Compositional Plumes

Abstract

The stability of a fully developed plume of compositionally buoyant fluid, of finite width, enclosed between two vertical boundaries and rising in a less buoyant infinite fluid is investigated. The plume and the outside fluid have the same thermal diffusivity, , material diffusivity, , and kinematic viscosity, . The linear stability problem is governed by four dimensionless parameters : the (Grashoff) Reynolds number , , where  and  are typical velocity and characteristic length  , respectively, the Prandtl number ,    , the Schmidt number ,  , and the dimensionless thickness of the Cartesian plume, . The stability analysis is examined in the case . It is found that the presence of diffusion of material introduces an extra term, , in the expression for the growth rate. The term  is found to be negative except in a small region of the wavenumber space where it is positive. The influence of  on the stability is examined to find that although material diffusion decreases the values of growth rate, the plume remains unstable for all values of the parameters of the dynamical system. Material diffusion is also found to affect the wavenumbers of the unstable mode; 3-dimensional modes can be transformed into 2-dimensional modes or vice versa by the presence of material diffusion.