Absolute and convective instabilities in turbulent gas-laminar liquid film flows

Gas-liquid flows are important from a fundamental fluid mechanics point of view, but are also central in a variety of engineering applications, such as distillation, absorption and cooling of electronic devices. Our prototypical system for such flows consists of a thin laminar liquid film flowing down an inclined plate in the presence of a countercurrent turbulent gas. The liquid flow is influenced by the gas through the tangential and normal stresses acting at the interface. We develop low-dimensional models for the liquid-flow problem: a long-wave model and a weighted integral-boundary layer (WIBL) model. These models, along with the Orr-Sommerfeld problem derived from the full Navier-Stokes equations and associated boundary conditions are used to explore the linear stability of the liquid-gas system. For a given liquid flow rate, we show that the wave velocity decreases with increasing gas shear before changing direction at the ``flooding point.'' The appearance of this point is linked to the onset of absolute instability, where a localized disturbance gets amplified and contaminates the whole domain. This is also marked by the collision of two spatial branches at a saddle point. We supplement our stability analysis with time-dependent computations of the WIBL model.