Numerical Study of Turbulent Channel Flow over Surfaces with Variable Spanwise Heterogeneities: Topographically-driven Secondary Flows Affect Outer-layer Similarity of Turbulent Length Scales

Abstract

Wall-bounded turbulent flows over surfaces with spanwise heterogeneous surface roughness – that is, spanwise-adjacent patches of relatively high and low roughness – exhibit mean flow phenomena entirely different to what would otherwise exist in the absence of spanwise heterogeneity. In the outer layer, mean counter-rotating rolls occupy the depth of the flow, and are positioned such that “upwelling” and “downwelling” occurs above the low and high roughness, respectively. It has been comprehensively shown that these secondary flows are Prandtl’s secondary flow of the second kind (Anderson et al., J. Fluid Mech. 768, 316–347 2015). This behaviour indicates that spanwise spacing, s y , between adjacent patches of high and low roughness is, itself, a problem parameter; in this study, we have systematically assessed how s y affects turbulence structure in high Reynolds number channel flows via two-point correlations. “High roughness” is imposed with streamwise-aligned pyramid elements with height, h, selected to be ≈ 5% of the channel half height, H. For $s_{y}/H \gtrsim 1$ , we find that the aforementioned domain-scale mean circulations exist and the surface may be regarded as a topography. For s y /H ≲ 0.2, turbulence statistics show characteristics very similar to a homogeneous roughness and thus the surface may be regarded as a roughness. For 0.2 ≲ s y /H ≲ 2, the spatial extent of the counter-rotating rolls is controlled by proximity to adjacent rows, and we define such surfaces as being intermediate. We refer to such surfaces as intermediate state.