Resolvent-based estimation of turbulent wakes

This study employs a resolvent-based approach to estimate turbulent fluctuations in the near-wake of a spanwise-periodic NACA0012 airfoil at Ma = 0.3, Re = 23,000, and α = 6^○. To overcome the challenge posed by the global instability of a linearized Navier-Stokes operator, we use a data-driven approach for obtaining optimal resolvent-based kernels for flow estimation. The data are obtained from a large-eddy simulation and are used to compute cross-spectra that appear in the estimation kernels. The Wiener-Hopf formalism is then used to enforce causality in the kernels, making them applicable for real-time estimation. By construction, the kernels include the impact of the colored statistics of nonlinear terms from the Navier-Stokes equations that act as a forcing on the linear dynamics. Additionally, we explore optimal sensor placement by leveraging a priori error estimates and the low computational cost of building the resolvent-based kernels. Finally, our results demonstrate the effectiveness of the resolvent-based approach in estimating turbulent fluctuations in the wake of the airfoil.