The eddies are attached, but it is all right

Abstract

The behavior of velocity fluctuations near a wall has long fascinated the turbulence community, because the prevalent theoretical framework of an attached-eddy hierarchy appears to predict infinite intensities as the Reynolds number tends to infinity. Although an unbounded infinite limit is not a problem in itself, it raises the possibility of unfamiliar phenomena when the Reynolds number is large, and has motivated attempts to avoid it. We review the subject and point to possible pitfalls stemming from uncritical extrapolation from low Reynolds numbers, or from an over-simplification of the multiscale nature of turbulence. It is shown that large attached eddies dominate the high-Reynolds-number regime of the near-wall layer, and that they behave differently from smaller-scale ones. In that limit, the near-wall layer is controlled by the outer flow, the large-scale fluctuations reduce to a local modulation of the near-wall flow by a variable friction velocity, and the kinetic-energy peak is substituted by a deeper structure with a secondary outer maximum. The friction velocity is then not necessarily the best velocity scale. While the near-wall energy peak probably becomes unbounded in wall units, it almost surely tends to zero when expressed in terms of the outer driving velocity.