Non-linear forcing and triadic interactions in flows over spanwise periodic transpiration as a model for wall roughness*

Turbulent flows over spanwise periodic surface features are of great interest to many engineering applications, and we seek to shed light on the role of the non-linear terms in these flows. Direct numerical simulations (DNS) with streamwise aligned transpiration boundary conditions (Flores and Jimenez, JFM, 2006) are used to study the effect of spanwise periodicity. DNS of turbulent channel flows with wall transpiration at different spanwise wavenumbers are conducted at friction Reynolds number of 550. Similarities and differences between the flows are examined through the energy spectra of the forcing and the triadic interactions. The forcing spectra show similar structures between the flow with and without transpiration when the 2D mean profiles are used. Additionally, projection coefficients are defined to highlight the relative importance of each triadically compatible pair of wavenumbers. These projection coefficients identify three important regions of interactions between different scales similar to those employed by the generalized quasilinear (GQL) approximation (Marston et al., PRL, 2016).