Optimized eddy-viscosity models for coherent structures in turbulent jets

The inclusion of eddy-viscosity models in resolvent analyses of turbulent jets gives dominant modes that compare favorably to observed structures. In previous studies only a limited region of the flow parameter space has been examined. In this study, we investigate the effects of different azimuthal modes and regions of the jet that had not been considered previously. We determine an optimal eddy-viscosity field by applying a Lagrangian optimization framework that maximizes the projection between resolvent analysis and spectral proper orthogonal decomposition (SPOD) modes determined from a large-eddy-simulation database for a round Mach 0.4 jet. We find that while the optimal eddy viscosity substantially improves the agreement between the resolvent and SPOD modes for all frequencies investigated (i.e., low to moderate frequencies), the improvements are inferior to those of the axisymmetric modes. As the first and second helical modes contain the most energetic structures at these frequencies, determination of a more effective turbulence model is important for predictive models. We investigate some alternatives suggested by the data.