On the self-sustained nature of Townsend's attached eddies in wall-bounded turbulent flows
Résumé
More than fifty years ago Townsend proposed that the dynamics of wall-bounded turbulent flows is associated, at least statistically, to a family of coherent motions which are self-similar in the logarithmic layer. Since then, a long quest for the identification of these structures and of their dynamics has captivated generations of fluid dynamicists. For a long time the most widespread wisdom has been that Townsend's attached eddies consist of Λ-vortices, with kinetic energy produced by the smallest ones, living in the buffer layer, and then transferred to the, larger, logarithmic-layer ones and finally to the largest ones associated to large-scale (LSM) and very-large scale motions (VLSM).
In the talk I will summarize the results of ten years of investigations proposing an alternative view of the nature of Townsend's attached eddies. Evidence will be shown of the existence of a whole family of self-sustaining motions with scales ranging from those of buffer-layer streaks to those of large-scale and very-large-scale motions in the outer layer. It will be discussed how these motions, associated with streaks and quasi-streamwise vortices, are able to sustain themselves at each relevant scale in the absence of forcing from larger- or smaller-scale motions by extracting energy from the mean flow via a coherent lift-up effect . I will claim that these self-sustained motions are the long-sought Towsend's attached eddies. I will also discuss how invariant solutions of the filtered Navier–Stokes equations (the `large-eddy exact coherent structures') can be computed taking into full account the Reynolds stresses associated with smaller-scale motions. These exact solutions embed the coherent self-sustaining process and might play an important role in unravelling the chaotic dynamics of the single-scale coherent self-sustained motions.