Modeling roughness sublayer turbulence using resolvent analysis

Prediction of turbulent flow physics and mean quantities (e.g. drag) over general engineering-relevant rough surfaces remains an open research area. In previous work, resolvent analysis has been shown to predict flow features representative of the near-wall cycle in turbulent flows over smooth surfaces, and experimental measurements suggest agreement between resolvent mode representations and features in the temporally-averaged flow over sinusoidal roughness geometry (Caltech Thesis, Morgan 2019). In this study, local resolvent analysis is applied to the turbulent flow over a sand-grain geometry as a proxy for engineering-relevant roughness, and its efficacy for flow predictions is evaluated. The ability of local resolvent analysis to predict wake field and roughness sublayer turbulent motions is demonstrated through comparison with spectral proper orthogonal decomposition and temporally-averaged data from DNS of a turbulent channel flow with roughness resolved using an immersed boundary method. Low order resolvent mode representations reproduce the surface geometry and dispersive terms with sufficient fidelity to inform an iterative estimation method for the mean flow and hydrodynamic drag.