Coherent structures in a non-equilibrium large-velocity-defect turbulent boundary layer

The characteristics of the coherent structures in a strongly decelerated largevelocity-defect boundary layer are analysed by direct numerical simulation. The simulated boundary layer starts as a zero-pressure-gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain, in the form of a very thin separation bubble. The Reynolds number at separation is Re¿ = 3912 and the shape factor H = 3.43. The three-dimensional spatial correlations of (u, u) and (u, v) are investigated and compared to those of a zero-pressure-gradient boundary layer and another strongly decelerated boundary layer. These velocity pairs lose coherence in the streamwise and spanwise directions as the velocity defect increases. In the outer region, the shape of the correlations suggest that large-scale u structures are less streamwise elongated and more inclined with respect to the wall in large-defect boundary layers. The three-dimensional properties of sweeps and ejections are characterized for the first time in both the zeropressure-gradient and adverse-pressure-gradient boundary layers, following the method of Lozano-Duran et al. (J. Fluid Mech. ´ 694, 100–130, 2012). Although longer sweeps and ejections are found in the zero-pressure-gradient boundary layer, with ejections reaching streamwise lengths of 5 boundary layer thicknesses, the sweeps and ejections tend to be bigger in the adverse-pressure-gradient boundary layer. Moreover, small near-wall sweeps and ejections are much less numerous in the large-defect boundary layer. Large sweeps and ejections that reach the wall region (wall-attached) are also less numerous, less streamwise elongated and they occupy less space than in the zero-pressure-gradient boundary layer

Outer scales and parameters of adverse-pressure-gradient turbulent boundary layers

A clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers is established in this paper based on basic principles and theory, and the help of six adverse-pressure-gradient turbulent boundary layer databases and a zero-pressure-gradient one. Outer velocity and length scales for the mean velocity defect and the Reynolds stresses are discussed first. The conditions of validity of four velocity scales are determined in terms of the shape factor, since one scale is restricted to small velocity-defect boundary layers (the friction velocity ), one to large-defect ones (the pressure-gradient velocity ), while the two others are proper scales for all velocity-defect conditions (the Zagarola–Smits velocity and the mixing-layer-type velocity ). The turbulent boundary layer equations are then used to bring out, in a consistent manner and without assuming any self-similar behaviour, a set of non-dimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. In terms of a generic outer length scale and velocity scale , these non-dimensional parameters are the pressure-gradient parameter , the Reynolds number and the inertial parameter , where and are respectively the streamwise and wall-normal components of mean velocity at the boundary layer edge. These parameters have a clear physical meaning: they are ratios of the order of magnitude of forces, with the Reynolds shear stress gradient (apparent turbulent force) as the reference force – inertial to apparent turbulent forces for , pressure to apparent turbulent forces for and apparent turbulent to viscous forces for . We discuss at length their significance and determine under what conditions they retain their meaning depending on the outer velocity scale that is considered. The seven boundary layer databases are analysed and compared using the established framework. An astonishing and impressive result is obtained: by choosing , the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with , and in all these flows – not just the order of magnitude of these ratios. This cannot be achieved with and , and only imperfectly with . Consequently, , and can be used to follow – in a global sense – the streamwise evolution of the streamwise mean momentum balance in the outer region

Turbulent boundary layers and channels at moderate Reynolds numbers

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/¿=0.3¿0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Re¿ ¿ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/