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

双流体剪切流动在工程和环境流体力学中普遍存在。例子包括空气动力学中除冰剂上方的边界层，利用外部气流剪切的液体膜进行表面冷却，以及大气边界层与海浪的相互作用。这两种流体流动的不稳定性非常明显：气动升力和阻力取决于翼型周围边界层的状态，剪切膜的冷却速度取决于流动中的扰动水平，海浪的不稳定性导致破裂和海喷。本文研究了不同粘度和密度薄膜上边界层的正则问题。流动受到自由流湍流的影响，类似于在工程和环境流动中观察到的情况。这种相互作用导致层流边界层以一种称为旁路跃迁的方式分解为混沌或湍流状态。在提出的研究中，比较了在存在和不存在底层薄膜的情况下边界层的稳定性。可以预期，根据薄膜的性质，可以加速或延迟对湍流的分解。由于湍流增强了混合，从而导致粘性阻力，因此我们的兴趣在于过渡延迟，这可以通过减少阻力来节省大量成本。研究将包括两个部分：微扰分析和数值模拟。分析将集中在流动扰动与两种流体边界层之间相互作用的基本方面，例如，两种流体之间存在的界面如何影响涡旋扰动。模拟将提供一个数值实验室，模拟从层流到湍流的整个非线性击穿过程，并量化底层膜的作用。分析和数值方法的结合将提供自由流扰动与双流体边界层相互作用的全面视图。尽管重点是典型边界层问题，但所提出的框架是通用的，适用于许多其他工程和环境双流体剪切流动。

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.