Structured Input-Output Analysis of Turbulent Flows over Riblets

This paper applies structured input-output (I/O) methods to analyze turbulent channel flows over riblets. Structured I/O provides a reduced-complexity framework for accounting for the nonlinear terms in the Navier-Stokes equations, thus providing a greater degree of fidelity in the analysis of nonlinear flows than the related linear I/O and resolvent-based analysis techniques. We show that structured I/O is capable of predicting I/O gains relevant to the nonlinear flow physics as well as the associated modes that reveal the underlying instability mechanisms driving turbulent flows over riblets. Particularly, we show that the structured I/O analysis highlights dominant instabilities associated with the lift-up mechanism, Tollmien-Schlichting waves, and Kelvin-Helmholtz-type vortices for the turbulent channel flow model. The associated wavenumbers identified for these instabilities are physically consistent with the results found in prior DNS studies. Furthermore, we show that the rectangular and triangular riblets analyzed in this study minimize the I/O gains of the near-wall cycle, leading to the emergence of new smaller-scale structures that have been highlighted in previous DNS studies. Results and findings are reported and discussed for turbulent channel flows at 𝑅𝑒 𝜏 = 180 with smooth-walls and both rectangular and triangular riblet patterning.