## Abstract

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows-not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow-in a global sense-the streamwise evolution of the streamwise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

Original language | English |
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Title of host publication | Flow Manipulation and Active Control; Bio-Inspired Fluid Mechanics; Boundary Layer and High-Speed Flows; Fluids Engineering Education; Transport Phenomena in Energy Conversion and Mixing; Turbulent Flows; Vortex Dynamics; DNS/LES and Hybrid RANS/LES Methods; Fluid Structure Interaction; Fluid Dynamics of Wind Energy; Bubble, Droplet, and Aerosol Dynamics |

Publisher | American Society of Mechanical Engineers (ASME) |

ISBN (Electronic) | 9780791851555 |

DOIs | |

Publication status | Published - 2018 |

Event | ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting, FEDSM 2018 - Montreal, Canada Duration: 15 Jul 2018 → 20 Jul 2018 |

### Publication series

Name | American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM |
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Volume | 1 |

ISSN (Print) | 0888-8116 |

### Conference

Conference | ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting, FEDSM 2018 |
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Country/Territory | Canada |

City | Montreal |

Period | 15/07/18 → 20/07/18 |

### Bibliographical note

Publisher Copyright:Copyright © 2018 ASME.

### Funding

A.G.G. and Y.M. were supported respectively by ITU-BAP and NSERC of Canada. The computation of DNS2017 was made possible by a generous grant of computer time from Compute Canada. T.W. thanks the financial support of New Mexico Institute of Mining and Technology and Los Alamos National Laboratory.

Funders | Funder number |
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ITU-BAP | |

New Mexico Institute of Mining and Technology and Los Alamos National Laboratory | |

Natural Sciences and Engineering Research Council of Canada | DNS2017 |