Use of eddy viscosity in resolvent analysis of turbulent channel flow

Abstract

The predictions obtained from resolvent analysis with and without an eddy viscosity model for turbulent channel flow at Reτ=550 are compared to direct numerical simulation data to identify the scales and wave speeds for which resolvent analysis provides good predictions. The low-rank behavior of the standard resolvent identifies energetic regions of the flow whereas the eddy resolvent is low rank when the resulting projection of the leading eddy resolvent mode onto the leading mode from spectral proper orthogonal decomposition is maximum. The highest projections are obtained for structures that are associated with the near-wall cycle and structures that are energetic at z=±0.5. It is argued that these types of structures are likely to be correctly predicted for any friction Reynolds number due to the inner and outer scaling of the Cess eddy viscosity profile. The eddy resolvent also correctly identifies the most energetic wave speed for these two scales. For all other scales, neither analysis reliably predicts the most energetic wave speed or mode shapes. The standard resolvent tends to overestimate the most energetic wave speed while the eddy resolvent underestimates it. The resulting eddy resolvent modes are overly "attached"to the wall since the wall-normal gradient of the eddy viscosity overestimates the transport of energy towards the wall. These observations have direct implications for future work towards estimating turbulent channel flows using resolvent analysis and suggest that the Cess profile can be further optimized for individual scales to provide better low-order models of turbulent channel flows.