Viscous effect on absolute–convective instaiblity transition for the interface between coflowing gas and liquid streams

Interfacial instabilities in two-phase mixing layers play a central role in atomization and spray formation, where viscous effects and velocity contrast govern their dynamics. In this study, spatio-temporal viscous linear stability analysis (LSA) and two-dimensional interface-resolved numerical simulations are conducted to investigate the instability mechanisms, with the Reynolds number (Re) varied by systematically changing the gas viscosity. In the LSA, the Orr-Sommerfeld equation is solved to study spatio-temporal viscous instability modes. Two distinct saddle points for spatial branches are identified across a range of Re. The temporal growth rates corresponding to these saddle points exhibit non-monotonic variation with Re. Consequently, as gas viscosity increases and Re decreases, the instability transitions from a convective to an absolute regime and subsequently back to a convective regime. The energy budget is analyzed to elucidate the physics behind these transitions. At high Re, the upper branch is dominated by inviscid Reynolds stress in the gas phase. As Re decreases, viscous effects cause the upper branch to migrate to larger wave numbers, leading to a pinch with the lower branch, forming a saddle point and triggering a convective-to-absolute transition. As Re continues to decrease, the interfacial velocity of the mean flow increases significantly, pushing the lower branch, corresponding to upstream-propagating perturbations, away from the upper branch. This results in the disappearance of the saddle point and an absolute-to-convective transition. These transitions, driven by variations in gas viscosity and Re, are further confirmed by the numerical simulation results.