On the generation of instabilities in variable density flow

Interfacial or fingering instabilities have been studied recently in relation to contamination problems where a more dense plume is enclosed by and is moving along in a body of less dense fluid. Instabilities can play an important role in the mixing or dispersion process. Through the use of a variable density flow and transport code, we were able to study how the style of interfacial perturbation controls the pattern of instability development. Whether initial perturbations grow or decay depends mainly on the wavelength of the perturbing function. A critical perturbation wavelength must be exceeded for a perturbation to grow; otherwise the perturbation simply decays. Our work confirms earlier analyses that suggest that all stratified systems are inherently unstable, given some spectrum of the perturbing waves that exceed the critical wavelength. By implication, Rayleigh number stability criteria are inappropriate for evaluating the dense plume problem. Our study also demonstrates how numerical errors in a mass transport code can serve as a perturbing function and lead to the development of instabilities. However, these instabilities are not physically realistic and are essentially uncontrollable because their character depends on the extent to which numerical errors develop, as evidenced by the grid Peclet and Courant numbers.