Modelling the meandering secondary flow over spanwise periodic roughness

Turbulent flow over heterogeneous roughness is of great importance to many engineering applications. Meandering secondary flows have been observed in experimental studies with spanwise varying roughness (Wangsawijaya et al., JFM, 2020). We seek to shed light on the origin of the meandering behavior by understanding the linear and non-linear interactions that drive this feature. Transpiration boundary conditions (Flores and Jimenez, JFM, 2006) are used to mimic the behavior of spanwise periodic roughness. Direct numerical simulations (DNS) of turbulent channel flow with transpiration at the walls are conducted at friction Reynolds number of 550 and show similar meandering secondary flow as observed in the experiments. The DNS snapshots are also Fourier transformed in time to enable direct comparison with the mode-by-mode analysis of the resolvent framework. The triadic interactions between compatible modes are analyzed and used to inform the construction of a 2D resolvent analysis (Chavarin and Luhar, AIAA Journal, 2020), where the spanwise periodic 2D mean profile is used. The 2D resolvent analysis is able to capture the dominant features of the flow at significantly reduced computation cost compared to the DNS.