Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

Abstract

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Kármán "constant," the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

On the Formation Mechanisms of Artificially Generated High Reynolds Number Turbulent Boundary Layers

“…Assuming Taylor hypothesis for the convection velocity, u c (y) = u(y), a length scale is defined for each frequency, f , as λ = u c /f , which in wall units results λ + = λu τ /ν. The natural case follows the expected trend with Reynolds number: At low Re there is just one scale in the flow associated with the inner peak (collapsing at y + = 15 and λ + = 1000 as mentioned in Marusic et al (2010) for instance) and the production of turbulent kinetic energy near the wall. With increasing Re the separation of scales becomes more evident leading to an external zone of high energy content located around y/δ ∼ 0.06 i.e.…”

“…With increasing Re the separation of scales becomes more evident leading to an external zone of high energy content located around y/δ ∼ 0.06 i.e. the middle of the logarithmic law (Marusic et al 2010). In the case of the distorted boundary-layer two different behaviours are present.…”

“…This necessity for highly reliable high Re experiments and simulations in wall-bounded flows has been assessed in the last few years, e.g. Marusic et al (2010) or Klewicki (2010) amongst others. Given that, for existing computational facilities, the achievable Re in direct numerical simulation is lower than in experiments, several research groups have the objective of obtaining and studying high fidelity high Re experiments.…”

Numerical Studies of Quantum Turbulence

“…The study found that the mean flow of the superfluid component obeys a logarithmic profile of the distance from the solid wall, i.e., the log-law. The log-law is famous in field of a classical turbulence, which is confirmed by theoretical analysis [9,36], experiments [76,90], and numerical studies [92]. We briefly describe the basics of the logarithmic velocity profile in classical turbulence, followed by our numerical studies in quantum turbulence.…”

Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

“…For experiments in which the terrain was flat and the surface cover was uniform, these mechanisms may include detached eddies generated by shearing motions in the neutral boundary layer, convective motion in the outer layer of the convective boundary layer, and attached eddies initiated by instabilities within the atmopsheric surface layer [8,[43][44][45]. Even for neutral conditions, laboratory studies have also documented the impingement of large (and very large) structures onto the 'logarithmic' region at high Reynolds number [46][47][48]. Clearly, these largescale processes cause non-universal departure from inertial subrange scaling in both E(K) and F T T (K), and introduce low-frequency modulations in F wT (K) that must be included.…”