# A model for periodic structures in turbulent boundary layers

## Abstract

Many experimental studies emphasize the importance of periodic recognizable flow patterns for the transport process in turbulent flow. In this paper a model is formulated for the large scale part of the turbulent motion. The experimental observation that the structures in the outer region run in phase with the bursting cycle in the wall layer forms the basis of the model. The wall layer, where viscous stresses are important and the outer region where the inviscid approximation holds, are treated separately. The small scale part of the turbulent motion, which is assumed to be important in localized regions only (bursts regions), couples the wall region and the outer region.

The mean wall shear stress calculated with this model agrees reasonably well with the empirical formulae for the friction coefficient even for the more complex case of the transpired boundary layer. The main conclusion of the model calculations is that the transport of momentum can be very well explained in terms of turbulent structures. The model clearly illustrates how momentum is transported in three stages: (i) Thin elongated layers near the wall slow down as the result of viscous forces. (ii) The retarded fluid-is ejected in localized regions or bursts. (iii) The large scale motion in the outer region takes over the transport.

In this paper special attention will be given to the function of the longitudinal vortices in the wall layer. In turns out that they hardly influence the turbulent exchange, but that they are very important for the creation of locally unstable regions. It is believed that the strength of the longitudinal vortices is influenced by the large scale structures in the outer region. By this mechanism the large scales in the outer region can influence the burst frequency.

In a discussion some ideas are presented about what this can mean for special flow phenomena as: drag reduction by polymer solutions or along compliant walls and rapid shear stress change along curved walls.

## Keywords

Wall Shear Stress Large Eddy Simulation Turbulent Boundary Layer Outer Region Wall Region## Preview

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