## Abstract

The mean stress is one of the most important quantities of interest in turbulent boundary layers. The governing equations for the mean flow are used to derive a relation between the mean total stress and the mean velocity in a zero pressure gradient turbulent boundary layer, allowing the mean shear stress to be written as a function of wall-normal distance. The relation contains an unknown term, which is modeled using a linear function of the wall-normal distance, inspired by existing data sets. The model for the mean total stress requires the wall-normal mean velocity profile, which requires modeling if not available. The existing data sets and scaling arguments are used to obtain a simple and compact fit for the mean wall-normal velocity, which is subsequently used to obtain a simple model for the mean total stress. The model shows good agreement with the available simulation and experimental data for a large range of Reynolds number.

Original language | English (US) |
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Article number | 024603 |

Journal | Physical Review Fluids |

Volume | 6 |

Issue number | 2 |

DOIs | |

State | Published - Feb 10 2021 |

### Bibliographical note

Funding Information:This work is supported by ONR Grant No. N00014-20-1-2717. The authors thank Dr. P. Schlatter and Dr. J. Jiménez for making their simulation data available publicly .

Publisher Copyright:

© 2021 American Physical Society.

Copyright:

Copyright 2021 Elsevier B.V., All rights reserved.