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 the Kelvin-Helmholtz instability that develops in the flow of two superposed layers of a pure incompressible fluid and a fluid containing gas bubbles, coflowing with different velocities. We show that the presence of bubbles in one layer stabilizes the flow in some intervals of wavelengths.