Vortical Mode Interactions and Bypass Transition Delay in Two-Fluid Boundary Layers

Two-fluid shear flows are ubiquitous in engineering and environmental fluid mechanics. Examples include the boundary layer above deicing agents in aerodynamics, surface cooling using a liquid film sheared by an external gas flow, and the interaction the atmospheric boundary layer with ocean waves. The instability of these two-fluid flows is clearly significant: the aerodynamic lift and drag depend on the state of the boundary layer around the airfoil, the cooling rate of sheared films depends on the disturbance level in the flow, and the instability of ocean waves leads to breakdown and sea sprays.In this proposal, the canonical problem of a boundary layer above a film of different viscosity and density is studied. The flow is subjected to free-stream turbulence, similar to what is observed in engineering and environmental flows. This interaction causes a laminar boundary layer to breakdown to a chaotic, or turbulent, state in a manner known as bypass transition. In the proposed research, the stability of the boundary layer is compared in the presence and absence of an underlying film. It is expected that, depending on the properties of the film, the breakdown to turbulence can be accelerated or delayed. Since turbulence enhances mixing and, as a result, viscous drag, our interest is in transition delay which can lead to significant cost savings via drag reduction. The research will include two components: perturbation analysis and numerical simulations. The analysis will focus on fundamental aspects of the interaction between flow disturbances and the two-fluid boundary layer, for example how a vortical perturbation is affected by the presence of the interface between the two fluids. The simulations will provide a numerical laboratory where the full non-linear breakdown process from laminar to turbulence is simulated, and the role of the underlying film quantified. The combination of the analytical and numerical approaches will provide a comprehensive view of the interaction of free-stream perturbations with the two-fluid boundary layer. Despite the focus on the canonical boundary layer problem, the proposed framework is general and is applicable to a host of other engineering and environmental two-fluid shear flows.