1. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ = 1928 Figure Legend:

2. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ = 1928 Figure Legend:

3. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ = 5024 Figure Legend:

4. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ = 6662 Figure Legend:

5. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ = 6662 Figure Legend:

6. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ = 31,000 Figure Legend:

7. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ = 31,000 Figure Legend:

8. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Reθ versus Rex Figure Legend:

9. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Accumulated skin friction coefficient: computation (solid line), empirical line according to the formula in Eq. (3) (dashed line), and Blasius analytical laminar boundary layer line (dashed-dotted line) Figure Legend:

10. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 The computed value of von Kármán constant as a function of Reθ Figure Legend:

11. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profiles in wall coordinates for Reθ = 53 to 5.79 ×10 5, and universal profile according to solution of Eq. (51) Figure Legend:

12. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ ≃ 2900 Figure Legend:

13. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ = 5024 Figure Legend:

14. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ = 23,119 Figure Legend:

15. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Scaled viscous stress and scaled Reynolds shear stress versus y+, Reθ = 23,119 Figure Legend:

16. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Local skin friction coefficient: computation (solid line), Eq. (44) from George [38] (dashed line), experimental measurements of Österlund [7] (diamonds), De Graaff and Eaton [25] (circles), and Blasius analytical laminar boundary layer line (dashed-dotted line) Figure Legend:

17. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Reynolds number based on boundary layer thickness, present computation (solid line), Prandtl's empirical relationship in Eq. (46) (dashed-dotted line), Blasius laminar flow solution in Eq. (45) (dashed line) Figure Legend:

18. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 George and Castillo scaling law, computed (solid line), Österlund's experiment at Reθ = 2532 (plus), Österlund's experiment at Reθ = 5156 (circle), Österlund's experiment at Reθ = 10,161 (triangle), Österlund's experiment at Reθ = 25,779 (diamond) Figure Legend:

19. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Ratio of the viscous stress gradient and the Reynolds stress gradient with various Reynolds numbers Figure Legend:

20. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Mean velocity profile, Reθ ≃ 2900 Figure Legend:

21. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Reynolds shear stress profiles in wall coordinates, Reθ = 2,391 - 5.79 × 105, and universal profile according to the formula in Eq. (52) Figure Legend:

22. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Four-layer-region of a flat plate boundary layer at Reθ = 7.13 × 104 Figure Legend:

23. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 von Kármán scaling law, computed (solid line), Österlund's experiment at Reθ = 2532 (plus), Österlund's experiment at Reθ = 5156 (circle), Österlund's experiment at Reθ = 10,161 (triangle), Österlund's experiment at Reθ = 25,779 (diamond) Figure Legend:

24. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient J. Fluids Eng. 2014;136(3):031103-031103-16. doi:10.1115/1.4026418 Zagarola and Smits scaling law, computed (solid line), Österlund's experiment at Reθ = 2532 (plus), Österlund's experiment at Reθ = 5156 (circle), Österlund's experiment at Reθ = 10,161 (triangle), Österlund's experiment at Reθ = 25,779 (diamond) Figure Legend: