Component-wise outer similarity of turbulent boundary layers with strong adverse-pressure gradient
Abstract
The adverse-pressure-gradient (APG) effect challenges the classical scaling of turbulent boundary layers (TBLs) over a flat plate, and it remains unclear whether outer-layer similarity holds across a wide range of APG strengths.We assemble a benchmark comprising the present direct numerical simulation of a suction--blowing-induced separation bubble and published profiles, spanning Clauser parameters βe=0.04--$180$ and Reynolds numbers Reθ=530--$19000$. Across this broad (βe,Reθ) parameter range, existing APG normalizations do not simultaneously collapse the two mean-velocity defects and four Reynolds-stress components, leaving open whether outer similarity persists. Instead of defining new scalings, we normalize each quantity by its value at a common location ys. Results are shown using ys=0.5δ, beyond the outer stress peaks. For each of the six quantities, the normalized profiles exhibit a common outer shape across the conditions, with collapse emerging for y/δ≳0.2 for the velocity defects and y/δ≳0.4 for the Reynolds stresses. The collapse-error analysis shows that outer self-similarity is retained over a broad range of ys within the outer region and is not restricted to ys=0.5δ. Furthermore, explicit expressions are provided for the normalized outer profiles. These results support component-wise outer similarity under strong APGs and provide compact references for APG turbulence-model assessment and conditional profile reconstruction.
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BibTeX
@misc{shi2026componentwise,
title = {{Component-wise outer similarity of turbulent boundary layers with strong adverse-pressure gradient}},
author = {Yu-Xuan Shi and Mingze Ma and Xi Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20372},
eprint = {2610.20372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20372},
}
RIS
TY - UNPB
TI - Component-wise outer similarity of turbulent boundary layers with strong adverse-pressure gradient
AU - Yu-Xuan Shi
AU - Mingze Ma
AU - Xi Chen
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20372
UR - https://arxiv.org/abs/2610.20372
AB - The adverse-pressure-gradient (APG) effect challenges the classical scaling of turbulent boundary layers (TBLs) over a flat plate, and it remains unclear whether outer-layer similarity holds across a wide range of APG strengths.We assemble a benchmark comprising the present direct numerical simulation of a suction--blowing-induced separation bubble and published profiles, spanning Clauser parameters β_e=0.04--$180$ and Reynolds numbers Re_θ=530--$19000$. Across this broad (β_e,Re_θ) parameter range, existing APG normalizations do not simultaneously collapse the two mean-velocity defects and four Reynolds-stress components, leaving open whether outer similarity persists. Instead of defining new scalings, we normalize each quantity by its value at a common location y_s. Results are shown using y_s=0.5δ, beyond the outer stress peaks. For each of the six quantities, the normalized profiles exhibit a common outer shape across the conditions, with collapse emerging for y/δ≳0.2 for the velocity defects and y/δ≳0.4 for the Reynolds stresses. The collapse-error analysis shows that outer self-similarity is retained over a broad range of y_s within the outer region and is not restricted to y_s=0.5δ. Furthermore, explicit expressions are provided for the normalized outer profiles. These results support component-wise outer similarity under strong APGs and provide compact references for APG turbulence-model assessment and conditional profile reconstruction.
ER -