Flow structures and shear-stress predictions in the turbulent channel flow over an anisotropic porous wall

Abstract

This article identifies the main coherent structures driving the flow dynamics in the turbulent channel flow over anisotropic porous walls. Two different cases have been analyzed where the drag increases or decreases with respect to a channel with isotropic porous walls. Higher order dynamic mode decomposition (HODMD) is applied to analyze these data, identifying 20 and 15 high amplitude modes in the drag increasing (DI) and drag reducing (DR) cases, respectively, which well reflects the largest flow complexity in the former case. The frequency of 13 modes and the three-dimensional structure of the modes are similar in the DR and DI cases, suggesting the need of using more complex analyses to deepen our physical insight of these flows. The spatio-temporal HODMD analysis identifies a periodic solution along the spanwise direction (as imposed by the boundary conditions). The wavenumbers related to the modes with highest amplitude are β = 0 and β = 3 (Lz = 2 3 π ). The rollers, groups of spanwise correlated structures, are mostly identified in the DI case near the wall, with β = 0, while the presence of the streaks, streamwise correlated structures are mostly identified in the DR case. Although, in areas far away from the wall it is possible to identify these two types of structures with β = 3 in both cases, depending on the temporal frequency of the DMD modes, the rollers and the streaks are related to high and low frequency DMD modes, respectively. Finally, a model is constructed to predict the temporal evolution of the wall shear, using the 6 most relevant DMD modes interacting near the channel wall: 6 low frequency modes for DR and 3 low and 3 high frequency modes for DI. In the DR case the wall shear is predicted for almost 300 time units with relative error ∼ 2%, however, this error is larger in the DI case, ∼ 6%, suggesting the need of using a larger number of modes to represent this more complex flow.