Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent-incoherent interaction is lumped into a Reynolds averaged Navier-Stokes (RANS) eddy viscosity model, and the mean-coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantic-Lugo & Gallaire (2016 J. Fluid Mech. 793, 777-797. (doi:10.1017/jfm.2016.109)). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.