Coherent structures in turbulence and Prandtl's mixing length theory (27th Ludwig Prandtl Memorial Lecture)
Abstract
The fundamental ideas behind Prandtl's famous mixing length theory are discussed in the light of newer findings from experimental and theoretical research on coherent turbulence structures in the region near solid walls. A simple theoretical model for 'flat' structures is used to examine the fundamental assumptions behind Prandtl's theory. The model is validated by comparisons with conditionally sampled velocity data obtained in recent channel flow experiments. Particular attention is given to the role of pressure fluctuations on the evolution of flat eddies. The validity of Prandtl's assumption that an element of fluid retains its streamwise momentum as it is moved around by turbulence is confirmed for flat eddies. It is demonstrated that spanwise pressure gradients give rise to a contribution to the vertical displacement of a fluid element which is proportional to the distance from the wall. This contribution is particularly important for eddies that are highly elongated in the streamwise direction.
 Publication:

Zeitschrift fur Flugwissenschaften und Weltraumforschung
 Pub Date:
 August 1984
 Bibcode:
 1984ZFlWe...8..233L
 Keywords:

 Mixing Length Flow Theory;
 Reynolds Stress;
 Shear Flow;
 Turbulent Flow;
 Vortices;
 Wall Flow;
 Cartesian Coordinates;
 Flow Visualization;
 Poisson Equation;
 Fluid Mechanics and Heat Transfer