Triglobal resolvent analysis of separated flow around a NACA0012 finite wing: Reynolds number effects

Resolvent analysis offers valuable insights into flow unsteadiness and the design of flow control techniques. In this study, we employ triglobal resolvent analysis to investigate the effects of Reynolds numbers Re∈[600;5000] on separated flow over a NACA0012 finite wing of semi-aspect-ratio sAR=2 and at an angle of attack α=14°. Depending on the Reynolds number, the time-averaged base flow is obtained by direct numerical simulations or wall-resolved large eddy simulations. Our focus is on understanding the influence of Reynolds number on the response and forcing modes, as well as the energy gain associated with different frequencies. For all the Reynolds numbers investigated, we observe a shift of the modal structures toward the outboard region as the forcing frequency increases, consistent with observations at lower Reynolds numbers. Furthermore, we find that sufficiently strong tip vortices support modal structures at the highest frequencies. We also show that varying the forcing frequency causes the modal structures to change their inclination relative to the wing span. In particular, the maximum energy gain is achieved for structures that are parallel to the wing and at forcing frequencies that increase with the Reynolds number. In this regard, we propose a Reynolds number-based normalization for the mechanisms driving the most energetic dynamics, providing a more comprehensive understanding of the flow behavior across different Reynolds numbers.