Reconsiderations about inner layer of wall-bounded flows

TL;DR

This paper revises the model of the extended overlap region in wall-bounded flows, emphasizing a universal inner layer coefficient and analyzing the agreement of viscous and inviscid models with experimental and DNS data near the wall.

Contribution

It introduces a revised model distinguishing inner and overlap layers with universal and flow-dependent coefficients, and reevaluates models using data closer to the wall where viscous effects are significant.

Findings

The inner layer coefficient k_in is universal, approximately 0.38-0.39.

The overlap layer coefficient k_o depends on flow pressure gradient.

Both viscous and inviscid models fit experimental data well near the wall.

Abstract

Following recent evidence that even ZPG boundary layers do not exhibit a purely logarithmic extended overlap region, reconsideration of recently advanced logarithmic plus linear extended overlap region in wall-bounded flows leads to a revision of the model for the extended overlap region. The significant difference between the two representations is a separation between the inner layer and the extended overlap layer in the coefficient of the logarithmic term into $\kappa_{in}$ and k_o, respectively. From a wide range of data examined in wall-bounded flows, the value of k_in is universal and equal to 1/2.6 or in the range 0.38<k_in<0.39. The value of k_o depends on the pressure gradient imposed by the flow geometry. In regard to the trends of the streamwise normal stress, recent publications concluded that the defect-power model developed from bounded dissipation is in more agreement with experimental data from ZPG boundary layers and pipe flows, as well as DNS data for channel and pipe flows, than the logarithmic model developed with inviscid analysis based on wall-scaled eddies. For some recent investigations and the entire previous literature on this popular topic, the assessment is made in the overlap region between inner and outer flows, which has limited viscous effects and is essentially inviscid; i.e., y+_in>400 and Y_out~0.45. This appears to be counterintuitive and deserves further attention. Here, both models are reevaluated using the same data sets from recent investigations in a region closer to the wall but outside the region with viscous stresses exceeding 20% of the total stress; i.e., dominated by viscous effects. It is perplexing that both an inviscid and a viscous model agree equally well with experiments and DNS data in this region closer to the wall.