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Control of the buffer and logarithmic layers in wall-bounded turbulent flows



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This thesis studies the effect of controlling separately the buffer and logarithmic layers in wall-bounded turbulent flows.

In the case of buffer-layer control, we examine the effect on near-wall turbulence of displacing the apparent, virtual origins perceived by different components of the overlying flow. This mechanism is commonly reported for drag-altering textured surfaces of small size. For the particular case of riblets, it has been proposed that their effect on the overlying flow could be reduced to an offset between the origins perceived by the streamwise and spanwise velocities, with the latter being the origin perceived by turbulence. Later results, particularly in the context of superhydrophobic surfaces, suggest that this effect is not determined by the apparent origins of the tangential velocities alone, but also by the one for the wall-normal velocity. To investigate this, we conduct direct simulations of turbulent channels imposing different virtual origins for all three velocity components using Robin, slip-like boundary conditions. The results of our simulations support the idea that the relevant parameter is the offset between the virtual origins perceived by the mean flow and turbulence. When using Robin, slip-like boundary conditions, the virtual origin for the mean flow is determined by the streamwise slip length. Meanwhile, the virtual origin for turbulence results from the combined effect of the wall-normal and spanwise slip lengths. The slip experienced by the streamwise velocity fluctuations, in turn, has a negligible effect on the virtual origin for turbulence, and hence the drag, at least in the regime of drag reduction. This suggests that the origin perceived by the quasi-streamwise vortices, which induce the cross-flow velocities at the surface, is key in determining the virtual origin for turbulence, while that perceived by the near-wall streaks, which are associated with the streamwise velocity fluctuations, plays a secondary role. In this framework, the changes in turbulent quantities typically reported in the flow-control literature are shown to be merely a result of the choice of origin, and are absent when using as origin the one experienced by turbulence. Other than this shift in origin, we demonstrate that turbulence thus remains essentially smooth-wall-like. A simple expression can predict the virtual origin for turbulence in this regime. The effect can also be reproduced a priori by introducing the virtual origins into a smooth-wall eddy-viscosity framework. We also present exploratory results that suggest that the effect on the flow of opposition control, an active flow-control technique, can also be interpreted in terms of virtual origins.

In the second part of this thesis, we investigate the effect of controlling the flow within the logarithmic layer alone, without directly modifying the flow elsewhere, and assess how this effect varies with Reynolds number. In contrast to buffer-layer control strategies, controlling the logarithmic layer has the potential to provide a reduction in turbulent drag that does not diminish with increasing Reynolds number. We first consider the effect of an idealised, hypothetical control strategy that is able to remove all of the Reynolds shear stress in all or part of the logarithmic layer, while leaving the rest of the flow unaltered. The idea is that this would serve as a theoretical prediction for the maximum turbulent drag reduction achievable by strategies that target the logarithmic layer alone. We quantify the effect of this control strategy on the flow and find that by relaminarising the whole logarithmic layer or a fixed portion of it in outer units, it is theoretically possible to produce a reduction in drag that improves with increasing Reynolds number. We also conduct a series of direct numerical simulations of turbulent channel flows at friction Reynolds numbers in the range 360 ≲ Reτ ≲ 2000, and artificially remove certain streamwise and spanwise wavelengths of the wall-normal velocity across a range of heights primarily within the logarithmic layer. The aim is to inhibit the dynamics of the self-similar, wall-attached sweep and ejection motions and their associated vortex clusters that reside in the logarithmic layer, while modifying the near-wall dynamics as little as possible. When these wavelengths are removed, we observe a positive, outward shift in the mean velocity profile, due to a local reduction in Reynolds shear stress, and subsequent increase in viscous stress, within the controlled region. When a fixed proportion of the uncontrolled Reynolds shear stress is removed across the whole logarithmic layer in our simulations, we show that it is possible to generate a reduction in drag that improves with Reynolds number, although the idealised control strategy grossly over-predicts the actual performance. This occurs because the majority of the energy originally contained in the removed scales in the control region is redistributed to even larger scales, rather than eradicated. This suggests that the flow in the logarithmic layer is very robust, even to this kind of targeted control strategy. Therefore, even though controlling the logarithmic layer has significant potential in theory, our results suggest that actual performance may be limited.





Garcia Mayoral, Ricardo


flow control, wall-bounded turbulence, drag reduction


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
EPSRC (1965893)
Engineering and Physical Sciences Research Council (1965893)