Log-linear law of the mean streamwise velocity in turbulent boundary layers with moderate adverse pressure gradients

Fuente: arXiv
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Main Authors: Lyu, Fuzhou, Zhao, Lihao, Huang, Weixi, Xu, Chunxiao
Format: Preprint
Published: 2026
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author Lyu, Fuzhou
Zhao, Lihao
Huang, Weixi
Xu, Chunxiao
author_facet Lyu, Fuzhou
Zhao, Lihao
Huang, Weixi
Xu, Chunxiao
contents An essential feature of canonical zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs) is that the mean streamwise velocity exhibits a logarithmic dependence on the wall-normal distance, known as the log law. In this study, we demonstrate that this conventional log law is not suitable for turbulent boundary layers subjected to pressure gradients (PGs). Instead, a log--linear law is theoretically derived for TBLs under moderate adverse pressure gradients (APGs), based on the total shear-stress balance and a rescaled eddy-viscosity model. The validity of the proposed log--linear law is assessed using available datasets of incompressible APG TBLs with the Clauser pressure-gradient parameter $β$ ranging from 0.73 to 9.0. Compared with the conventional log law, the present log--linear formulation shows significantly improved agreement with the measured mean velocity profiles. In the limiting case of $β\to 0$, the proposed law naturally recovers the classical log law.
format Preprint
id arxiv_https___arxiv_org_abs_2601_18087
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Log-linear law of the mean streamwise velocity in turbulent boundary layers with moderate adverse pressure gradients
Lyu, Fuzhou
Zhao, Lihao
Huang, Weixi
Xu, Chunxiao
Fluid Dynamics
An essential feature of canonical zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs) is that the mean streamwise velocity exhibits a logarithmic dependence on the wall-normal distance, known as the log law. In this study, we demonstrate that this conventional log law is not suitable for turbulent boundary layers subjected to pressure gradients (PGs). Instead, a log--linear law is theoretically derived for TBLs under moderate adverse pressure gradients (APGs), based on the total shear-stress balance and a rescaled eddy-viscosity model. The validity of the proposed log--linear law is assessed using available datasets of incompressible APG TBLs with the Clauser pressure-gradient parameter $β$ ranging from 0.73 to 9.0. Compared with the conventional log law, the present log--linear formulation shows significantly improved agreement with the measured mean velocity profiles. In the limiting case of $β\to 0$, the proposed law naturally recovers the classical log law.
title Log-linear law of the mean streamwise velocity in turbulent boundary layers with moderate adverse pressure gradients
topic Fluid Dynamics
url https://arxiv.org/abs/2601.18087