Optimal Riblet Spacing for Turbulent Flows Determined by Rank-1 Structured Input/Output Analysis*

Patterned riblet surfaces have demonstrated the potential to passively reduce turbulent drag. Turbulent flows over riblets can be modelled and observed through structured input/output (I/O) analysis. Our work exploits recent theoretical advances to impose more precise nonlinear structure I/O analyses within structured I/O analysis. Our implementation reduces computational complexity by leveraging a rank-1 approximation of the linear dynamics, which then acts in feedback with a frozen flow field that results in maximum energy amplification of flow perturbations. Initial results suggest that imposing the more precise structure results in identification of instability mechanisms that are consistent with observations in prior direct numerical simulations. The optimal riblet spacing for a rectangular riblet geometry is identified for an incompressible channel flow at friction Reynolds number 180. The results are compared against predictions made using resolvent analysis and direct numerical simulations.