Nonlinear shape evolution of immiscible two-phase interface

The Kelvin-Helmholtz (KH) instability is one of the most elementary and widespread models of fluid dynamics. The model is successful in predicting several physical situations, although in its basic formulation it does not consider the finite thickness of the shear layer and the nonlinear saturation of the exponential amplification of disturbances. However, there are flow configurations, such as those of fuel injection systems, where the basic KH linear model fails because the nonlinear effects play a major role in the process of transition from stratified to slug flow, and therefore the finite amplitude of the instability wave has to be taken into account starting from the early instants. Previous contributions of literature are due to Orazzo et al., for non-parallel channel shear flow, and to Hoepffner et al., for unconfined flows and disturbance wave produced by a localized impulse force. In both cases, the relevant characteristic of the inherently nonlinear instability is the emergence of a single travelling wave, whose characteristic velocity is different from the one of the classic linear KH theory. In the present work, visualizations of a nonlinear Kelvin-Helmoltz instability is obtained via direct numerical simulations of the Navier-Stokes equations for a gas-liquid flow confined in a channel. Simulations are performed by means of the interFoam solver, based on the volume of fluid (VOF) method. The code is included within the open-source package OpenFOAM and is widely validated for the flows of interest. The different features that distinguish the single-wave scenario from the classical train of KH linear waves are highlighted and discussed in the paper.