Effect of a 2-D rough wall on the anisotropy of a turbulent channel flow

The effects of 2-D roughness elements on the Reynolds stress anisotropy tensor, b(ij) (=(u(i)u(j)/q)-(1/3)delta(ij), where u(i)u(j) is the Reynolds stress tensor, q = u(i)u(i) and delta(ij) the Kronecker delta symbol) in a turbulent channel flow are investigated using data obtained from direct numerical simulations (DNSs). The roughness elements consist of transverse square rods with a size k and are placed on one wall of the channel only. While k is kept constant (k/h = 0.2, h is the half-width of the channel), the spacing, w, between the rods is varied from w/k = 1 to w/k = 39. The results show that the 2-D roughness dramatically changes the structure of the wall region flow, and that the changes are controlled by w/k. In terms of turbulence modelling, they indicate that the modelling of the near-wall region needs to reflect both the structural changes and the influence of w/k on these changes. Possible forms of models are discussed.