Von Karman constant

The constant A in Eq. 10.2.20 is the von Karman constant, equal to 0.4. Though the Prandtl mixing length hypothesis (Eq. 10.2.20) works for conditions in the turbulent core... 

The parameter k is called the von Karman constant, and the value that fits most of the data is 0.41. The corresponding value of B is 5.0. Intermediate between these layers is the buffer layer, where both shear mechanisms are important. The essential feature of this data correlation is that the wall shear completely controls the turbulent boundary layer velocity distribution in the vicinity of the wall. So dominant is the effect of the wall shear that even when pressure gradients along the surface are present, the velocity distributions near the surface are essentially coincident with the data obtained on plates with uniform surface pressure [82]. Within this region for a flat plate, the local shear stress remains within about 10 percent of the surface shear stress. It is noted that this shear variation is often ignored in turbulent boundary layer theory. 

The integration constant in (16.62) has been evaluated experimentally for smooth surfaces and has been found to be equal to 5.5. The constant k is known as the von Karman constant with a value of 0.4. In spite of an uncertainty of the order of 5% in empirical estimates of k for different surfaces, it is considered a universal constant. The mean velocity profile can therefore be calculated by... 

Dispersion Curves and the Bom-von Karman Constants 1179 Table 12.1 The Born-von Karman force constants for sodium at temperature 90 K (after [9]). 

The two-layer turbulence model with only one adjustable parameter, the von Karman constant tc, was found to be promising in describing the DR effect, although it does not include the anisotropy of the turbulence. Validation calculations against measurements in pipe flow show a good agreement. First simulations of the measurement apparatus demonstrate that the experimental results can be used to infer the dependence of k on the relevant physical parameters. 

The extent by which the Von Karman constant is suppressed by turbulence is difficult to assess. 

Ippen (1971) conducted an analysis of turbulent suspensions in open channel flows. This work showed that the concentration close to the lower boundary was the most important factor suppressing the Von Karman constant. This may not be astonishing when we consider that beds of coarse particles form in this region at low speeds. 

Suspended load reduced the value of the Von Karman constant. Values of Aj. between 0.314 and 0.342 were measured (by comparison with 0.4 for full pipes). The reduction of the Von Karman coefficient indicated a reduced level of mixing and a tendency by the sediments to suppress turbulence. 

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