The Prandtl mixing length and the spectrum of the turbulent shear stress
Abstract
The equation for turbulent shear stress in turbulent shear flows was obtained by Prandtl in 1925 with the aid of a model regarding the displacement of turbulence elements from one layer to another. Prandtl's derivations lead to the logarithmic form of the law of the wall. An improved relation for shear flows was obtained by Prandtl in 1942. Developments concerning a formulation for the turbulent momentum transport which takes into account the totality of turbulent shear flows were reported by Prandtl (1954) and Kolmogorov (1942). The significance of the various relations is investigated, giving attention to the spectral distributions of the turbulent shear stress in the boundary layer at the planar plate.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 September 1978
 DOI:
 10.1002/zamm.19780580912
 Bibcode:
 1978ZaMM...58..418S
 Keywords:

 Boundary Layer Flow;
 Mixing Length Flow Theory;
 Prandtl Number;
 Shear Stress;
 Turbulent Boundary Layer;
 Laminar Flow;
 Spectral Energy Distribution;
 Wall Flow;
 Fluid Mechanics and Heat Transfer