Unsteady Dynamics of Free-Interface Gravitational Liquid Sheet Flows

. Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r ρ of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as r ρ increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713 , 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.