A new upward-convective short-wave instability mode in gas-sheared falling liquid films

We investigate a short-wave instability mode recently identified via temporal stability analysis in weakly inclined falling liquid films sheared by a confined turbulent counter-current gas flow (Ishimura et al. J. Fluid Mech. vol. 971, 2023, p. A37). We perform spatio-temporal linear stability calculations based on the Navier–Stokes equations in the liquid film and the Reynolds-averaged Navier–Stokes equations in the gas, and compare these with our own experiments. We find that the short-wave instability mode is always upward-convective. The range of unstable group velocities is very wide and largely coincides with negative values of the wave velocity. Turbulence affects this mode both through the level of gas shear stress imparted and via the shape of the primary-flow gas velocity profile. Beyond a critical value of the counter-current gas flow rate, the short-wave mode merges with the long-wave Kapitza instability mode. The thus obtained merged mode is unstable for group velocities spanning from large negative to large positive values, i.e. it is absolute. The onset of the short-wave mode is precipitated by decreasing the channel height and inclination angle, and by increasing the liquid Reynolds number or the gas-to-liquid dynamic viscosity ratio. For vertically falling liquid films, merging occurs before the short-wave mode can become unstable on its own. Nonetheless, the ability to generate upward-travelling ripples is endowed to the merged mode. Preliminary calculations neglecting the linear perturbation of the turbulent viscosity suggest that three-dimensional perturbations could be more unstable than two-dimensional ones.