On the interfacial instabilities of two-phase wake and jet flows with density stratification and surface tension

The coexistence of density stratification and surface tension alters the dynamic behaviors of two-phase immiscible wake and jet flows in complex interfacial instability modes. Building on the framework established by Schmidt et al. [“Global stability and nonlinear dynamics of wake flows with a two-fluid interface,” J. Fluid Mech. 915, A96 (2021)], we conduct a global stability analysis to investigate the effects of surface tension and density ratio on the interfacial instabilities of two-phase planar wake and jet flows. Surface tension, acting counterintuitively as either a stabilizer or destabilizer, enhances the self-sustainability of varicose and sinuous disturbances at low levels, while high surface tension ultimately leads to the stabilization of interfacial disturbances. Additionally, sinuous disturbances, characterized by higher oscillation amplitudes, predominate in dense wakes or wakes with strong shear strengths, where surface tension serves exclusively as a stabilizing factor. In contrast, the varicose pattern in jets prevails over a wider range of Weber numbers, exhibiting relatively higher linear growth rates compared to their sinuous counterparts, especially in lighter jets. The temporal-spatial analysis further provides a theoretical demonstration of these findings by offering views into the complex interplay of these factors.