Two-Fluid Boundary Layer Stability

Abstract

The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode found in the classical hydrodynamical stability theory an additional Yih-mode exists due to the two-fluid interface. The effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-newtonian character of the lower fluid on the stability characteristics are determined, Also the mechanisms leading to instability for the two modes are reported. The results are compared with analytical, numerical and experimental results reported in the literature