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Turbulent Boundary Layer

The turbulent flow near solid boundaries is described by empirically-determined relationships called the Law of the wall. Measurements show, that for turbulent flows, the velocity near the wall varies logarithmically with the distance from the surface. From dimensional analysis^{23.2} we obtain the law of the wall:

(23.8)

where is Kármán’s constant and the quantity is known as the friction velocity:

(23.9)

Correlation of measurements indicate and .

Figure: A sketch of developed turbulent boundary layer in dimensionless coordinates and .

Figure () shows typical velocity profile for a turbulent boundary layer. The graph displays the dimensionless velocity, and dimensionless wall distance, defined as:

(23.10)

Finally, the Law of the wall can be described:

(23.11)

The fully developed boundary layer can be viewed as divided into four regions: Viscous sublayer is a region closest to the wall. In this region The fluid flow is always laminar here. The Viscous sublayer region is typically where .

Buffer layer is a region, where neither law holds. The Buffer layer region is typically where .

Logarithmic (Log-law) layer is a region, where the Law of the wall holds. The Log-law layer region is typically where .

Outer (Defect) layer is a region, where the free-stream is taking over. The Outer layer region is typically where .

Figure: A sketch of near wall detail of developed turbulent boundary layer in dimensionless coordinates and .