Von Kármán constant

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 (typically the value 0.41 is used), 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.

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.

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