Stability of shear flow of stratified fluids with fine dust

The linear stability of plane parallel shear flows of a stably stratified incompressible fluid laden with uniformly distributed fine dust particles is studied. It is shown that the Miles criterion for stability, the Rayleigh-Synge criterion for instability, and Howard's semicircle theorem can be extended under the assumptions that the mass concentration is very small and that the relaxation time of the dust particles is very much less than the time scale characterizing the basic flow. The effect of fine dust is found to increase the region of instability. In addition, a semi-ellipse criterion for instability has been given as an improvement over Howard's semicircle criterion. © 1981 American Institute of Physics.