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In fluid dynamics, the von Kármán constant , named for Theodore von Kármán, is a dimensionless constant involved in the logarithmic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent fluid flow near a boundary with a no-slip condition. The equation for such boundary layer flow profiles is:
where u is the mean flow velocity at height z above the boundary. The roughness height z0 is where u {\displaystyle u} appears to go to zero. Further κ is the von Kármán constant being typically 0.41, and u ⋆ {\displaystyle u_{\star }} is the friction velocity which depends on the shear stress τw at the boundary of the flow:
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.