Inner–outer interactions in rough-wall turbulence

Abstract

ABSTRACTHere we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u* signal does depend on roughness Reynolds number (k+s), but is robust to changes in friction Reynolds number (δ+). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.