Wall Curvature and Thermal Effects on 3-D Lagrangian Coherent Structures in a Supersonic, Turbulent Boundary Layer*

Compressible, spatially-evolving turbulent boundary layers are of great importance across civilian and military applications. Understanding transport phenomena is critical to efficient high-speed vehicle designs. Although at any instantaneous point in time a flow field may seem random, regions within the flow can exhibit coherency across space and time. These coherent structures play a key role in momentum and energy transport within the boundary layer. In this work, we focus on three-dimensional Lagrangian Coherent Structure (LCS) based on the finite-time Lyapunov exponent (FTLE) for three wall thermal conditions (cooling, quasi-adiabatic and heating). The flow is subject to a strong concave curvature (δ/R ≈ -0.083, δ is the boundary layer thickness and R is the curvature radius) followed by a very strong convex curvature (δ/R ≈ 0.17). A GPU-accelerated particle simulation forms the basis for the 3-D FTLE where particles are advected over flow fields obtained via Direct Numerical Simulation (DNS) with high spatial/temporal resolution. We have observed a growing anisotropic character in the coherent structures as wall cooling is applied. A high correlation is observed between ejection events, Q2, and attracting manifolds (backward time integration of particle's trajectories).