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:
where u is the mean flow velocity at height z above the boundary. The roughness height (also known as roughness length) z0 is where appears to go to zero. Further κ is the von Kármán constant (typically the value 0.41 is used), and 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.