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Scaling of velocity fluctuations in statistically unstable boundary-layer flows

Published online by Cambridge University Press:  08 January 2020

Xiang I. A. Yang Open the ORCID record for Xiang I. A. Yang [Opens in a new window] ,
Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]  and
Mahdi Abkar Open the ORCID record for Mahdi Abkar [Opens in a new window]
Xiang I. A. Yang
Affiliation:
Mechanical Engineering, Penn State University, State College, PA16802, USA
Sergio Pirozzoli
Affiliation:
Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, 00184Rome RM, Italy
Mahdi Abkar*
Affiliation:
Department of Engineering, Aarhus University, 8000Aarhus C, Denmark
*
†Email address for correspondence: abkar@eng.au.dk
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Abstract

Much of our theoretical understanding of statistically stable and unstable flows is from the classical Monin–Obukhov similarity theory: the theory predicts the scaling of the mean flow well, but its prediction of the turbulent fluctuation is far from satisfactory. This study builds on Monin–Obukhov similarity theory and Townsend’s attached-eddy hypothesis. We present a model that connects the mean flow and the streamwise velocity fluctuations in both neutral and unstable boundary-layer flows at both moderate and high Reynolds numbers. The model predictions are compared to direct numerical simulations of weakly unstable boundary layers at moderate Reynolds numbers, and large-eddy simulations of unstable boundary-layer flows at high Reynolds numbers. The flow is shear dominated. The range of stability parameter considered in this work is $L/\unicode[STIX]{x1D6FF}<-0.1$, where $L$ is the Monin–Obukhov length, and $\unicode[STIX]{x1D6FF}$ is the boundary-layer height. Reasonably good prediction of velocity fluctuations based on knowledge of the mean velocity profile is obtained.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A3
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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