Lyapunov spectrum of scale-resolving turbulent simulations. Application to chaotic adjoints

Abstract

We present an investigation of the Lyapunov spectrum of the chaotic, separated flow around the NACA 0012 airfoil at Reynolds number 2,400. The impact of the numerical discretization on the spectrum is investigated through time and space refinement studies. Numerical results show that the time discretization has a small impact on the Lyapunov exponents, whereas the spatial discretization can dramatically change them. In particular, the asymptotic Lyapunov spectrum for this wall-bounded flow is achieved with global CFL numbers as large as O(10¹−10²), whereas the system continues to become more and more chaotic as the mesh is refined even for meshes that are much finer than the best practice for this type of flows. Based on these results, we conclude the paper with a discussion on the feasibility of adjoint-based sensitivity analysis for chaotic flows.