Rayleigh–Taylor instabilities in miscible fluids with initially piecewise linear density profiles


Scott Cowell, Philip Trevelyan and James Kent have had a paper published in the Journal of Engineering Mathematics.

Abstract: In this study we consider a species dissolved in a fluid and examine the instabilities due to 

changes in the density profile. The growth of the instability depended on the distribution 

of the species. If the species is uniformly dissolved in an upper half and absent from the 

lower half, then perturbations grow like exp(ω T^(1/2) ) where ω is a constant and T is time. 

If the species is uniformly dissolved in a thick but finite layer, then eventually perturbations 

will grow algebraically. If the species is in a thick finite layer in which the density profile 

linearly decreases in the downwards direction then perturbations grow like exp(ω T) where 

ω is a constant and T is time, however, eventually the growth of the perturbations will slow
down and grow algebraically.