The dynamics of the outer region of wall-bounded turbulence : La dinámica de la zona exterior en la turbulencia de pared

Abstract

The objective of this thesis is the analysis of the dynamics of the outer region of wall-bounded flows, focusing on the interaction between the inner- and outer- layers. The primary tool used in the present study is a set of Direct Numerical Simulations (DNS) of turbulent channels with friction Reynolds number Reτ ≈ 630. In those simulations, the standard non-slip and impermeability boundary conditions are substituted by prescribed velocity disturbances that destroy the near-wall energy cycle characteristic smooth-walled flows. In this sense, the present DNSes can be understood as a simulation of a turbulent flow consisting on a core region without a near-wall region. The profiles of the mean velocity and of the velocity fluctuation intensity show similar effects as those reported on rough-walled flows, and our wall- forcing corresponds to equivalent sand roughness in the fully rough regime. The changes on the flow structure imposed by the wall forcing are essentially limited to the roughness sublayer; a layer near the wall whose height is proportional to a length scale defined in terms of the additional Reynolds stresses. The spectral distribution of energy in this layer is dominated by the wavenumber of the velocity disturbances and by its harmonics. Outside of it, only the largest scales of the flow are modified by the wall forcing. They are the global modes identified in previous works, corresponding to structures highly correlated from the wall to the center of the channel. Our results indicate that their intensity does not scale with the friction velocity, nor with the centerline velocity. However, a velocity scale proporional to uτ log(Reτ ) is able to collapse of the velocity fluctuations of several wall-bounded turbulent flows over a wide range of Reynolds numbers and surface roughness. Similar conclusions are drawn from the analysis of the coherent structures of vor ticity that populate the logarithmic and outer regions of the wall-disturbed cases. The attached clusters have the same properties over smooth and rough walls, and in both cases they make important contributions to the Reynolds stress in the logarithmic and outer regions. In average, the attached clusters are statistically associated with wall-normal velocity bursts and cone-shaped streaks of low-momentum fluid. Our results indicate that the global modes are connected to the part of these streaks that have sizes comparable to the flow thickness. They are very coherent motions, where the wall-normal and streamwise velocity components are tightly coupled. The final part of this thesis puts together all those observations into a linear model that explains the generation of the cone-shaped low-speed streaks of the loga rithmic region by bursts of wall-normal velocity. The results of the linear simulations show that localized bursts generate elongated upstream u-streaks that agree well with the velocity fields conditioned to attached clusters, but where the downstream wakes observed in real turbulent flows are absent. The absence of the downstream part of the low-momentum cones suggests that the cones are the cause, rather than the effect, of the bursts. It is hypothesized that the burst are generated by some instability of the local velocity profile, in analogy with the near-wall cycle. However, while the near-wall cycle is autonomous, the effect of the outer region has to be included in the model in order to generate strong enough streaks. This suggests that the causality assumed in most models of wall-bounded turbulence could be reversed, and that the outer region may be critical for the dynamics of the logarithmic layer.