The dynamics of thin gas layer moving between two fluids

Abstract

The dynamics and stability of a thin gas layer moving between two fluid layers moving in the same or opposite direction is studied. The linear evolutionary equations describing the spatial-temporal dynamics of the interface perturbations between gas and two fluid layers are derived for the flat two-dimensional case. Integral correlations across the layer are obtained, and the various kinds of time dependent base states are found. A linear stability is considered for the system using non-stationary equation array derived. The equation array consists of the two one-dimensional non-stationary equations of a seventh and fourth order. The results of the numerical study of the governing evolution equations support the results of the analysis for more simple limit cases. It is found that the thin sheet gas flow in-between two liquid layers is unstable and the peculiarities are found and discussed together with some applications available.