Harmonic turbulent stress budgets in forced transonic flow over a bump

The transonic flow over a bump is studied using implicit large-eddy simulations. To replicate rotor/stator interactions occurring in turbomachinery, harmonic forcing of the backpressure is imposed at the outlet. Various perturbation frequencies are prescribed and encompass different regimes, from a fully locked configuration to a decoupling between the unperturbed and forced flows. The mean solution is, however, found to be independent of the perturbation. In a triple-decomposition framework, the coherent component of the flow is extracted by phase averaging. Organized structures of streamwise velocity and turbulence kinetic energy are highlighted. Whereas these structures are of similar shapes beneath the shock system, their extent in the downstream boundary layer is controlled by the frequency of the perturbation. The mean and harmonic turbulent stress budgets are presented. A typical three-peak distribution of mean turbulent diffusion is reported, which is also found to appear for coherent turbulent diffusion. Harmonic production arises mainly from the mean shear and its modulation.