References

[1] L. Prandtl, “Über Flüssigkeitsbewegung bei sehr kleiner Reibung,” in Verhandlungen es Dritten Internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer, ed., Teubner, Leipzig, Germany (1905), p. 484.

[2] H. Schlichting, Boundary-Layer Theory, 7th ed., McGraw-Hill, New York, 1979.

[3] D. Weyburne, “A Boundary Layer Model for Unbounded Flow Along a Wall,” Air ForceTech Report: AFRL-RY-WP-TR-2020-0004, https://discover.dtic.mil, Accession # AD1091170 , 2020.

[4] D. Weyburne, “The Unbounded and Bounded Boundary Layer Models for Flow Along a Wall,” Air Force Tech Report: AFRL-RY-WP-TR-2020-0005, https://discover.dtic.mil, Accession # Accession # AD1094086 , 2020.

[5] D. Weyburne, “A New Conceptual Model for Laminar Boundary Layer Flow,” Air Force Tech Report: AFRL-RY-WP-TR-2020-0006, https://discover.dtic.mil, Accession #AD1091187 , 2020.

[6] D. Weyburne, "A mathematical description of the fluid boundary layer," Applied Mathematics and Computation, 175, 1675(2006). Also D. Weyburne, Erratum, Applied Mathematics and Computation, 197, 466(2008).

[7] D. Weyburne, “New Shape Parameters for the Laminar, Transitional, and Turbulent Velocity Profiles,” Air Force Tech Report: AFRL-RY-HS-TR-2010-0016, https://discover.dtic.mil/, Accession # ADA519321, 2010.

[8] D. Weyburne, “New thickness and shape parameters for the boundary layer velocity profile,” Experimental Thermal and Fluid Science, 54, 22(2014).

[9] H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,“ Zeitschrift für Mathematik und Physik, 56, 1(1908).

[10] R. Swanson and S. Langer, “Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods,” NASA/TM-2016-219003.

[11] P. Roach and D. Brierley, “The influence of a Turbulent Free Stream on Zero Pressure Gradient Transitional Boundary Layer Development,” in: O. Pirnneau, W. Rodi, I. Ryhming, A. Savill, and T. Truong (Eds.), Numerical Simulation of Unsteady Flows and Transition to Turbulence, Cambridge University Press, New York, 1992, pp 319-347. Data from https://www.ercoftac.org/.

[[12] See discussion in Wikipedia's Lift section. See also the discussion in the February 1, 2020 web article by Ed Regis or in NASA’s aerodynamic lift misconceptions website which can be found here. A YouTube video by Doug McLean on the problems with earlier lift explanations is available here.

[13] R. Örlü and P. Schlatter, “Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers,” Exp. Fluids, 43, 1547(2013).

[14] D. Weyburne, "Inner/Outer Ratio Similarity Scaling for 2-D Wall-bounded Turbulent Flows," arXiv:1705.02875 [physics.flu-dyn], 2017.

[15] J. Fürst, P. Straka, J. Příhoda, and D. Šimurda, “Comparison of several models of the laminar/turbulent transition,” EPJ WebofConferences, 45, 01032 (2013).

[16] F. Menter, R. Lechner, and A. Matyushenko, “Best Practice: Generalized k-ω Two-Equation Turbulence Model in Ansys CFD (GEKO),” ANSYS Technical Report, 2020.

[17] P. Durbin, “Perspectives on the Phenomenology and Modeling of Boundary Layer Transition,” Flow, Turbulence and Combustion, 99, 1(2017).

[18] K. Avila, D. Moxey, A. de Lozar, M. Avila, D. Barkley, and B. Hof, “The Onset of Turbulence in Pipe Flow,” Science, 333, 192 (2011).

[19] D. Weyburne, "New thickness and shape parameters for describing the thermal boundary layer," arXiv:1704.01120 [physics.flu-dyn], 2018.

[20] E. Pohlhausen, “Der wärmeaustausch zwischen festen körpern und flüssigkeiten mit kleiner reibung und kleiner wärmeleitung,” Zeitschrift für Angewandte Mathematik und Mechanik, 1, 115(1921).

[21] J. Jovanović, B. Frohnapfel, E. Škaljić, and M. Jovanović, “Persistence of the Laminar Regime in a Flat Plate Boundary Layer at very High Reynolds Number,” Thermal Science, 10, 63(2006).

[22] U. Ghia, S. Bayyuk, S. Habchi, C. Roy, T. Shih, T. Conlisk, C. Hirsch, and J. Powers, “The AIAA code verification project - Testcases for CFD code validation,” AIAA 2010-0125, 2010.

[23] I. Nikuradse, Laminare Reibungsschichten an der längs angetrömten Platte. Monograph, Zentrale f. wiss. Berichtswesen, Berlin, 1942.

[24] J. Lewins, “Beyond the boundary layer: the Blasius paradox,” Int. J. Mech. Engr. Educ., 27, 55(1999).

[25] D. Weyburne, “The Normal to the Wall Pressure Gradient for Blasius and Falkner-Skan Boundary Layer Flow,” Air Force Tech Report AFRL-RY-WP-TR-2018-0153, https://discover.dtic.mil/, Accession # AD1063207, 2018.

[26] V. M. Falkner and S. Skan, Aero. Res. Coun. Rep. and Mem. no 1314, 1930.

[27] H. Schlichting and K. Gersten, Boundary-Layer Theory, 9^th edn., Springer, 2017.

[28] B. Munson, D. Young, T. Okiishi, and W. Huebsch, Fundamentals of Fluid Mechanics, 7^th edn., John Whiley and Sons, 2013.

[29] R. Panton, Incompressible Flow, 4th ed., John Wiley, New Jersey, 2013.

[30] D. Weyburne, “Similarity of the Velocity Profile,” AF Tech Report: AFRL-RY-WP-TR-2014-0221, https://discover.dtic.mil/, Accession # ADA609962, 2014.

[31] J. Rotta, "Turbulent Boundary Layers in Incompressible Flow," Prog. Aeronaut. Sci., 2, 1(1962).

[32] A. Townsend, The Structure of Turbulent Shear Flow, 2n ed. (Cambridge University Press,

Cambridge, 1956).

[33] L. Castillo and W. George, “Similarity Analysis for Turbulent Boundary Layer with Pressure Gradient: Outer Flow,” AIAA J., 39, 41(2001).

[34] V. Kitsois, A. Sekimoto, C. Atkinson, J. Sillero, G. Borrell, A. Gungor, J. Jiménez and J. Soria, "Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation," J. Fluid Mech., 829, 392(2017).

[35] D. Weyburne, “Does the Outer Region of the Turbulent Boundary Layer Display Similar Behavior?", arXiv:1706.05236 [physics.flu-dyn], 2017.

[36] D. Weyburne, "Similarity of the Temperature Profile formed by Fluid Flow along a Wall," arXiv:1603.05062 [physics.flu-dyn], 2018.

[37] I. Marusic, B. McKeon, P. Monkewitz, H. Nagib, A. J. Smits, and K. Sreenivasan, “Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues,” Phys. Fluids, 22, 065103 (2010).

[38] F. Clauser, "The turbulent boundary layer in adverse pressure gradients," J. Aeronaut. Sci. 21, 91(1954).

[39] M. Zagarola and A. Smits, “Mean-flow scaling of turbulent pipe flow,” J. Fluid Mech., 373, 33(1998). Also M. Zagarola, and A. Smits, “A New Mean Velocity Scaling for Turbulent Boundary Layers,” Proceedings of FEDSM’98, Washington D.C., 1998.

[40] D. Weyburne, "Are Defect Profile Similarity Criteria Different Than Velocity Profile Similarity Criteria for the Turbulent Boundary Layer?," arXiv:1510.05588v1 [physics.flu-dyn], 2015.

[41a] D. Weyburne, "The Prevalence of Similarity of the Turbulent Wall-bounded Velocity Profile," arXiv:1412.5129v5 [physics.flu-dyn], 2015.

[41b] D. Weyburne, "A Cautionary Note on the Zagarola and Smits Similarity Parameter for the Turbulent Boundary Layer, " arXiv:1507.06951 [physics.flu-dyn], 2017.

[42] R. Panton, “Review of wall turbulence as described by composite expansions,” Appl. Mech. Rev., 58, 1 (2005).

[43] M. Buschmann and M. Gad-el-Hak, “Recent developments in scaling of wall-bounded flows,” Prog. Aeronaut. Sci., 42, 419(2007).

[44] J. Österlund, PhD. Thesis, KTH Royal Institute of Technology, Stockholm, 1999.

[45] D. Weyburne, “Similarity of the Outer Region of the Turbulent Boundary Layer", Air Force Tech Report: AFRL-SN-HS-TR-2010-0013, https://discover.dtic.mil/, Accession # ADA519314, 2010.

[46] R. Smith, Ph. D. thesis, Princeton University, 1994.

[47] D. Weyburne,"A Cautionary Note on the Thermal Boundary Layer Similarity Scaling for the Turbulent Boundary Layer," arXiv:1603.07728 [physics.flu-dyn], 2016.

[48] X. Wang and L. Castillo, "Asymptotic solutions in forced convection turbulent boundary layers," J. of Turbulence, 4, 1(2003).

[49] J. Klewicki, P. Fife, T. Wei, and P. McMurtry, “A physical model of the turbulent boundary

layer consonant with mean momentum balance structure,” Phil. Trans. R. Soc. A, 365, 823(2007).

[50] I. Marusic, J. Monty, M. Hultmark, and A. Smits, “On the logarithmic region in wall turbulence,” J. Fluid Mech., 716, R3-2(2013).

[51] L. Prandtl, “Über die ausgebildeteTurbulenz,” ZAMM 5, 136(1925).

[52] T. von Kármán, "Mechanische Ähnlichkeit und Turbulenz", Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl., 5, 58(1930).

[53] R. Örlü, PhD Thesis, KTH Royal Institute of Technology, Stockholm, 2009.

[54] K. Chauhan, H. Nagib, and P. Monkewitz, in Progress in Turbulence 2. Proceedings of iTi Conference in Turbulence, edited by M. Oberlack, G. Khujadze, S. Guenther, T. Weller, M. Frewer, J. Peinke, and S. Barth _Springer, New York, pp. 159–163, 2007.

[55] H. Nagib and K. Chauhan, “Variations of von Kármán coefficient in canonical flows,” Phys. Fluids, 20, 101518 (2008).

[56] D. Weyburne, "The Origin of the Log Law Region for Wall-bounded Turbulent Boundary Layer Flows," Air Force Tech report: AFRL-RY-HS-TR-2011-0005, https://discover.dtic.mil/, Accession # ADA538378, 2011.

[57] D. Weyburne, "On the Origin of the Log Law Region: Instantaneous Velocity Profile Models." 6th AIAA Theoretical Fluid Mechanics Conference, 10.2514/6.2011-3931, 2011.

[58] S. Obi, K. Inoue, T. Furukawa, and S. Masuda, “Experimental study on the statistics of wall shear stress in turbulent channel flows,” Int. J. Heat and Fluid Flow, 17, 187(1996).

[59] C. Diaz-Daniel, S. Laizet, and J. Vassilicos, “Wall shear stress fluctuations: Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer,” Physics of Fluids, 29, 055102 (2017).

[50] X. Wu and P. Moin, “Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer,” J. Fluid Mech., 630, 5(2009).

[61] E. Winkel, J. Cutbirth, S. Ceccio, M. Perlin, D. Dowling, “Turbulence profiles from a smooth flat-plate turbulent boundary layer at high Reynolds number,” Exp. Thermal Fluid Sci., 40, 140(2012). Data corresponding to the LDV profiles at (x = 10.795 m, u_e = 6.69 m/s), (x = 10.795 m, u_e = 13.37 m/s), and (x = 10.795 m, u_e = 20.21 m/s).

[62] S. Bailey, M. Hultmark, J. Monty, P. Alfredsson, M. Chong, R. Duncan, J. Fransson, N. Hutchins, I. Marusic, B. McKeon, and H. Nagib, “Obtaining accurate mean velocity measurements in

high Reynolds number turbulent boundary layers using Pitot tubes,” J. of Fluid Mechanics, 715,642(2013). Data corresponding to Univ. Melbourne P.T. = 0.089.

[63] N. Hutchins, T. Nickels, I. Marusic, and M. Chong, “Hot-wire spatial resolution

issues in wall-bounded turbulence,” J. Fluid Mech., 635, 103(2009).

[64] M. Hultmark, M. Vallikivi, S. Bailey, and A. Smits, “Logarithmic scaling of turbulence in smooth-and rough-wall pipe flow,” J. Fluid Mech., 728, 376 (2013).

[65] S. Zimmerman, J. Philip, J. Monty, A. Talamelli, I. Marusic, B. Ganapathisubramani, and J. Klewicki, “A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to 10⁴,” J. Fluid Mech., 869, 182(2019) and R. Baidya, W. Baars, S. Zimmerman, M. Samie, R. Hearst, E. Dogan, J. Monty, “Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows,” J. Fluid Mech., 871, 377(2019). Data from https://www.euhit.org/projects/CASCADES.

[66] ES Zanoun, PhD Thesis, Univ. Erlangen-Nurnberg, Erlangen, 2003.

[67] G. El Khoury, P. Schlatter, A. Noorani, P. Fischer, G. Brethouwer, and A. Johansson, “Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers,” Flow Turbul. Combust., 91, 475(2013). Data supplied by the authors.

[68] D. Weyburne, "The Description and Scaling Behavior for the Inner Region of the Boundary Layer for 2-D Wall-bounded Flows," arXiv:1703.02092 [physics.flu-dyn], 2018.

[69] D. Weyburne, "The Prandtl Plus Scaling Failure and its Remedy," arXiv:1701.02364 [physics.flu-dyn], 2017.

[68] D. Weyburne, "The Prandtl Plus Scaling Approximation for Turbulent Boundary Layer Flows," arXiv:1708.03547 [physics.flu-dyn], 2017.

[70] M. Jones, T. Nickels, and I. Marusic, “On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer,” J. Fluid Mech., 616, 195(2008).

[71] R. Smith, Ph. D. thesis, Princeton University, 1994.