The interplay between large scales of motion and the wall shear stress in wall-bounded turbulence

Wall-bounded flows are flows of engineering interest in which a fluid flows in the proximity of a solid wall. Examples of wall-bounded flows are the flow of air (or water) around a moving (streamlined) vehicle, or the fluid flow inside a pipe. The fluid and the solid exchange a frictional force (or a stress, to be more precise) which takes the name of wall shear stress. The wall shear stress typically represents an expense for the flow, as for instance it slows down the moving vehicle or it slows down the fluid running inside the pipe. Wall-bounded flows are typically turbulent, meaning that a set of vortices of various sizes is found inside the flow; these vortices advect and distort each other in a chaotic manner. The vortices can be cathegorised into large and small scales of motion depending on how their size changes under changing circumstances (e.g. by increasing the flow velocity).
This manuscript deals with the effects produced by large turbulent vortices on the wall shear stress, and vice-versa with how large scales are influenced by the wall shear stress. This mutual interaction takes many forms. First off, the wall shear stress represents the main cost of driving a flow, and the share of costs caused by the presence of large scales is investigated. ... mehrMoreover, it is verified how much of these costs can be spared if the large scales are removed from the flow, e.g. by some flow control device. This can help understand whether controlling large scales is a viable cost-reducing strategy: so far, research on flow control has mainly focused on small scales, and the only commercially available flow control device (riblet films, to the author’s knowledge) works by targeting small scales indeed.
Additionally, the interaction between large scales and the wall shear stress is explored in terms of two mechanims concerning the dynamics of large scales. Shedding light on the dynamics of large scales could help both to improve turbulence models for large-eddy simulations and to design phyisically- informed large-scale flow control devices. Large scales typically reside further away from the wall than small ones; nevertheless, their footprint can be found in the near-wall region in the form of a large- scaled pattern of the wall shear stress (consisting in regions of higher- and lower-than-average wall shear stress). This pattern is commonly understood to locally distort the small scales in a process named amplitude modulation. To verify whether these distorsions are caused by the pattern of wall shear stress, a numerical experiment is designed, in which large scales are prevented from creating a footprint at the wall. Although the idea behind aplitude modulation is that large scales exert an influence on the near-wall region, a second mechanism is explored in this manuscript, according to which large scales might originate from near-wall flow features instead. As postulated by Townsend (The structure of turbulent shear flow, 2 nd ed., 1976), large-scaled patterns of wall shear stress might be able to trigger the formation of self-sustaining large-scaled motions. These motions are then able to become the dominant flow feature thanks to their extended life time. The plausibility of Townsend’s hypothesis is assessed by artificially triggering the formation of structures of a controlled size and then measuring their life time.