Prandtl mixing length (2) Turbulent boundary layer application

The mixing length theory is a turbulence theory developed by Ludwig Prandtl (Prandtl 1925). The mixing length lm is the characteristic distance travelled by a particle of fluid before its momentum is changed by the new environment
Let us consider a turbulent boundary layer. Because of boundary friction and the no slip condition, the velocity increases with increasing distance y away from and perpendicular to the plate. Considering the turbulent flow bounded by the solid boundary, i.e. the boundary layer flow bounded by the plate, the Prandlt mixing length may be assumed by be about: lm = K.y, where K is the von Karman constant (K =0.4). That is, the mixing length increases linearly with increasing distance y. Introducing the shear velocity, one can derive the well-known law of wall for the velocity profile in a developing turbulent boundary layer.
The Prandtl mixing length theory is a fundamental concept for turbulent boundary layer and shear flows in applied fluid mechanics and fluid dynamics. A basic understanding of the physical turbulent processes is critical in many real-word applications and discussed in a number of relevant KZbin video movies in the same Playlist at:
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Boundary layer (1) Presentation
Prandtl mixing length (1) Presentation
Acknowledgements
Professor Colin J. APELT
References
PRANDTL, L. (1925). "Über die ausgebildete Turbulenz." ('On Fully Developed Turbulence.').A.M.M., Vol. 5, pp. 136-139 (in German).
PRANDTL, L. (1952). "Essentials of Fluid Dynamics with Applications to Hydraulics, Aeronautics, Meteorology and Other Subjects." Blackie & Son, London, UK, 452 pages.
SCHLICHTING, H. (1979). "Boundary Layer Theory." McGraw-Hill, New York, USA, 7th edition.
CHANSON, H. (2014). "Applied Hydrodynamics: An Introduction." CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 448 pages & 21 video movies (ISBN 978-1-138-00093-3).
VOGEL-PRANDTL, J. (2014). "Ludwig Prandtl. A Personal Biography Drawn from Memories and Correspondence." Göttinger Klassiker der Strömungsmechanik, Universitätsverlag Göttingen, Germany, 263 pages (ISBN: 978-3-86395-160-3).