Reynolds and dispersive shear stress contributions above highly skewed roughness

Abstract

The roughness functions induced by irregular peak- and/or pit-dominated surfaces in a fully developed turbulent channel flow are studied by direct numerical simulation. A surface generation algorithm is used to synthesise an irregular Gaussian height map with periodic boundaries. The Gaussian height map is decomposed into ‘pits-only’ and ‘peaks-only’ components, which produces two additional surfaces with similar statistical properties, with the exception of skewness, which are equal and opposite $({\mathcal{S}}=\pm 1.6)$. While the peaks-only surface yields a roughness function comparable to that of the Gaussian surface, the pits-only surface exhibits a far weaker roughness effect. Analysis of results is aided by deriving an equation for the roughness function that quantitatively identifies the mechanisms of momentum loss and/or gain. The statistical contributions of ‘form-induced’ and stochastic fluid motions to the roughness function are examined in further detail using quadrant analyses. Above the Gaussian and peaks-only surfaces, the contributions of dispersive and Reynolds shear stresses show a compensating effect, whereas above the pits-only surface, an additive effect is observed. Overall, the results emphasise the sensitivity of the near-wall flow with respect to higher-order topographical parameters, which can, in turn, induce significant differences in the roughness function above a peak- and/or pit-dominated surface.