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Davide Selvatici
The turbulent flow over a curved wall is studied to investigate the scale-space effect of a small wall curvature on the structure of near-wall turbulence. The study relies on a direct numerical simulation database of an incompressible turbulent channel flow with a small concave-convex-concave bump placed on the lower wall. For the analysis we employ the Anisotropic Generalised Kolmogorov Equations (AGKE), i.e. the exact budget equation for the second-order structure function tensor, that describe production, redistribution, transport and dissipation of each component of the Reynolds stress tensor considering simultaneously the space of scales and the physical space, without any requirement of homogeneity and isotropy.
The bump affects the organisation of near-wall velocity fluctuations, yielding a favourable/adverse pressure gradient and a variable friction in the streamwise direction. Over the uphill bump side, the streaks of streamwise velocity are stretched in the spanwise direction and become weaker, as the energy drained from the mean field to sustain the streamwise velocity fluctuations decreases. After the bump tip, instead, the streaks become more vigorous and retrieve their characteristic spanwise scale, due to a more intense production mechanism. The presence of a curved wall also entails an exchange of vertical energy between the mean and the fluctuating field: over the uphill bump side energy is drained from the mean field to sustain the quasi-streamwise vortices, while over the downhill side the opposite occurs with energy going from the fluctuating to the mean field, except close to the wall. We have observed that over the upstream concave portion of the bump, close to the wall the fluctuations are organised in small-scale w−structures that are consistent with the presence of the Taylor-Görtler vortices. The AGKE analysis reveals that their dynamics is dominated by the pressure-strain term, as both their generation and their annihilation is accompanied by an intense energy redistribution.