Periodic Reporting for period 4 - COTURB (Coherent Structures in Wall-bounded Turbulence)
Periodo di rendicontazione: 2020-08-01 al 2021-07-31
Turbulence is a chaotic phenomenon for which control efforts have often failed because the number of degrees of freedom involved is large. However, kinetic energy and drag are controlled by relatively few slowly evolving large structures that sit on top of a multiscale cascade of smaller eddies. They are essentially single-scale phenomena whose evolution can be described using less information than for the full flow. In evolutionary terms they are ‘punctuated equilibria’ for which chaotic evolution is only intermittent. The rest of the time, they can be considered coherent and predictable for relatively long periods. Coherent structures studied in the 1970s in free-shear flows (e.g. jets) eventually led to increased understanding and to industrial applications. In wall-bounded flows (e.g. boundary layers or pipes), proposed structures range from exact permanent waves to qualitative hairpins or ejections. Although most of them have been described at low Reynolds numbers, there are reasons to believe that they persist at higher ones in the ‘LES’ sense in which small eddies are only treated statistically. Recent computational and experimental advances provide enough temporally and spatially resolved data to quantify the relevance of such models to fully developed flows. The idea of the project has been to use mostly existing numerical data bases to test the various models of wall-bounded coherent structures, to quantify how often and how closely the flow approaches them, and to develop moderate-time predictions. Existing solutions were to be extended to the LES equations, methods sought to identify them in fully turbulent flows, and reduced-order models developed and tested. In practical situations, the idea was to be able to detect large eddies and to predict them ‘most of the time’, and, if simple enough models could be found, implement the process in the laboratory and use it to suggest control strategies.
During the project, LES structures have been identified in several different flows, both theoretically and observationally, and the relations between these flows have been clarified. Reduced-order models have been generated, and it has been shown that these reduced representations can be detected from the wall, where practical observations are possible. The causal relations among different parts of the flow are also beginning to be understood. Control of the large coherent states was achieved in a computational model, with the unexpected result that the total drag increased, instead of decreasing. This was interpreted as a sign that, although coherent structures control the flow, they are too strong to be cheaply controlled. In essence they are too coherent to be a control target. A new direction of research directed towards identifying their presumably incoherent causal precursors has been developed, including machine-learning methods as part of the analysis.
The project has generated about 77 refereed and review papers, including those developed during the two international summer schools it has hosted, and four PhD theses.
The project has generated about 77 refereed and review papers, including those developed during the two international summer schools it has hosted, and four PhD theses.
Although future developments are always difficult to predict, there is a fair probability that control strategies can be identified, although it is now unlikely that they can exclusively address the coherent component of the flow.