Adjoint-based sensitivity analysis methods are powerful tools for engineers who use

ow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct numerical simula- tion (DNS), which exhibit the chaotic dynamics inherent in turbulent ows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by con- ventional methods, but has a high computational cost. The following report outlines a new, more computationally e cient formulation of LSS, non-intrusive LSS, and estimates its cost for several canonical ows using Lyapunov analysis.