Identification of very large scale structures in the boundary layer over large roughness elements

The dynamics of a turbulent boundary layer developing over a cube array is investigated based on stereoscopic PIV measurements performed in a boundary layer wind tunnel. The fluctuating streamwise velocity component u is analyzed via the recently introduced Spectral Proper Orthogonal Decomposition method (S-POD). A modification of the definition of the spatial S-POD modes is proposed so that they are orthonormal to each other. This results in spatio-temporal modes which reflect the statistical organization of the most energetic structures both in space and time. It is first demonstrated that the first S-POD modes of u correspond to large-scale elongated coherent structures of low or high momentum. The existence of very large scale structures whose length spans several boundary layer thickness is demonstrated, in agreement with the recent similar findings for flows over smooth wall. These structures are found to be non-negligible contributors to the Reynolds shear stress and the turbulent kinetic energy. Their relationship with the smaller scales of the flow is investigated via the computation of joint third-order statistics and is shown to be of non-linear nature. [GRAPHICS] .