A (disambiguation)

In fluid dynamics, the von Kármán constant (or Kármán constant), named for Theodore von Kármán, is a dimensionless constant describing the logarithmic velocity profile of a turbulent fluid flow near a boundary with a no-slip condition. The equation for such boundary layer flow profiles is:

$u=\frac{u_{\star }}{\kappa }\ln \frac{z}{z_0},$

where u is the mean flow velocity at height z above the boundary. The roughness height (also known as roughness length) z₀ is where $u$ appears to go to zero. Further κ is the von Kármán constant being typically 0.41, and $u_{\star }$ is the friction velocity which depends on the shear stress τ_w at the boundary of the flow:

$u_{\star }=\sqrt{\frac{{\tau }_w}{\rho }},$

with ρ the fluid density.

The Kármán constant is often used in turbulence modeling, for instance in boundary-layer meteorology to calculate fluxes of momentum, heat and moisture from the atmosphere to the land surface. It is considered to be a universal (κ = 0.41).

Gaudio, Miglio and Dey argued that the Kármán constant is however nonuniversal in flows over mobile sediment beds.

See also

• Law of the wall
• Log wind profile

References

• Bonan, G. B. (2005). "Land Surface Model (LSM 1.0) for Ecological, Hydrological, Atmospheric Studies. Model product". Available on-line [1] from Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, Tennessee, U.S.A.

• R. Gaudio, R. Miglio and S. Dey (2010). "Nonuniversality of von Kármán’s κ in fluvial streams". Journal of Hydraulic Research, International Association for Hydraulic Research (IAHR), Vol. 48, No. 5, 658-663

External links

• http://www.ccsm.ucar.edu/models/ccsm3.0/cpl6/users_guide/node21.html a list of physical constants used in the NCAR Community Climate System Model