Revisiting the law of the wake in wall turbulence

Abstract

The streamwise mean velocity profile in a turbulent boundary layer is classically described as the sum of a log law extending all the way to the edge of the boundary layer and a wake function. While there is theoretical support for the log law, the wake function, defined as the deviation of the measured velocity profile from the log law, is essentially an empirical fit and has no real physical underpinning. Here, we present a new physically motivated formulation of the velocity profile in the outer region, and hence for the wake function. In our approach, the entire flow is represented by a two-state model consisting of an inertial self-similar region designated as ‘pure wall flow state’ (featuring a log-law velocity distribution) and a free stream state, which results in a jump in velocity at the interface separating the two. We show that the model provides excellent agreement with the available high Reynolds number mean velocity profiles if this interface is assumed to fluctuate randomly about a mean position with a Gaussian distribution. The new concept can also be extended to internal geometries in the same form, again confirmed by the data. Furthermore, adopting the same interface distribution in a two-state model for the streamwise turbulent intensities, with unchanged parameters, also yields a reliable and consistent prediction for the decline in the outer region of these profiles in all geometries considered. Finally, we discuss differences between our model interface and the turbulent/non-turbulent interface (TNTI) in turbulent boundary layers. We physically interpret the two-state model as lumping the effects of internal shear layers and the TNTI into a single discontinuity at the interface.

Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers

“…They found that the elevated and recessed regions of the surface (corresponding to the LMPs and HMPs, respectively) resulted in low and high values of Π, respectively. As indicated by Krug, Philip & Marusic (2017), the wake strength parameter stems from a dual effect of the velocity jump across the TNTI as well as the uniform momentum zones. Therefore, the previously observed changes in the wake parameter are probably due to the changes in the intermittent activity across the span.…”

Scaling of velocity fluctuations in statistically unstable boundary-layer flows

“…Regarding the assumption (2.1), we note that eddies are not space filling in general, even in neutral boundary layers. Krug, Philip & Marusic (2017) showed that eddies may be non-space filling in the outer part of wall layers as a result of intrusions of free-stream fluid in boundary layers, and of quiescent core fluid in channel and pipe flows. Wu et al (2017) analysed direct numerical simulaation data of transitional boundary layers, and showed that eddies are not space filling both before and after transition, referring to those as turbulent-turbulent spots.…”

Reynolds-number independent inner-layer analytical formulation for type-A turbulent boundary layer based on DNS data

“…之后人们针对零压梯度半无限大 平板、直圆管和槽道湍流等一些比较简单的流动构 型, 应用平壁律进行了大量研究 [7][8][9] . [10][11][12][13][14][15][16][17][18][19] . 其中Xu等 人 [10][11][12] 基于对方、矩形环管DNS数据的深度分析, 给 出了对湍流边界层再认知和有关复杂几何流动壁面律 构建的新见解.…”

“…表征类-2湍流边界层内层的壁面律函数表达式 [12] . 而 本文采用了Schlatter, Örlü所给出的零压梯度平板 湍流DNS数据 [13][14][15][16][17] , 对平板流湍流边界内层进行了深 入剖析. 选取沿流动方向的10个不同雷诺数速度剖面…”

“…本文采用Schlatter和Örlü [13][14][15][16][17] (2) 边界层速度, 如时-空间平均摩擦速度u 和时均局 [21] ) 越来越强的加强或抑制效应. 借鉴Xu等人 [10][11][12] 对方、 矩形环管的类-2边界层分析, 其基本思想是通过中性…”