Bubble effect on Kelvin-Helmholtz' instability

We derive boundary conditions at interfaces (contact discontinuities) for a class of Lagrangian models describing, in particular, bubbly flows. We use these conditions to study Kelvin-Helmholtz' instability which develops in the flow of two superposed layers of a pure incompressible fluid and a fluid containing gas bubbles, co-flowing with different velocities. We show that the presence of bubbles in one layer stabilizes the flow in some intervals of wave lengths.