Evolution of a wave packet in nonuniform liquid sheets

The linear stability of a liquid sheet falling under gravity in a still gas is analyzed via wave packet solutions of the initial value problem. We study the sinuous disturbances responsible for the sheet break-up. As the gravity effect is fully considered, the basic flow is nonuniform, but spatially developing. The length scale over which the inertia-gravity effects become significant is far larger than the sheet thickness, suggesting a multiple scale approach; this makes for the local character of the system response to any given perturbation. The sheet undergoes a transition to a convective unstable behavior at a certain location along the streamwise direction. This critical distance from the slit exit section is a function of flow Weber number (independent of gas density). In the region closer to the slit, an algebraic growth is found which exhibits an absolutely unstable character. The time after which this occurs could be not sufficient to avoid the possible appearance of nonlinear phenomena to break up the sheet.