Revisiting the Law of the Wall in Fully Developed Turbulent Pipe and Channel Flows: A Compact Leading-Order and Explicit Reconstruction From Overlooked Phenomenological Insights and Freely Available Data

Motivated by increasing open access of direct numerical simulation (DNS) and experimental data, we discuss potentially overlooked phenomenological issues related to the formulation of a leading-order reconstruction of the law of the wall (LoW) in fully developed turbulent channel and pipe flows of constant fluid properties. Most of these issues relate to seemingly asymptotic constants or scalings evidenced in the available DNS data. These allow the derivation of a classical layer-based fit for the LoW of the mean velocity profile (MVP) in a clean and straightforward way. For low-to-moderate Reynolds number flows, the inherent empiricism due to incomplete similarity is handled by the specification of additional data-based correlations. As an example, the centerline velocity is required for the full specification of the MVP-LoW. We also discuss a novel layer-based fit for the wall-normal profiles of the turbulence kinetic energy (TKE) and the TKE-dissipation rate. The latter fits are mostly derived from DNS data, although we offer a series of novel insights, and we derive an overlooked scaling of the turbulence frequency which is related to our MVP-LoW. We consider the layer-wise LoW to be of relevance for the understanding of wall-bounded turbulence. Its closed and explicit form relying on very simple linear or quasi-linear fits renders it appealing for implementation in coarsely resolved Reynolds-Averaged Navier-Stokes (RANS) models for turbulent pipe and channel flows.