Von Kármán constant

In fluid dynamics, the von Kármán constant (or Kármán's 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 ${\displaystyle u}$ appears to go to zero. Further κ is the von Kármán constant being typically 0.41, and ${\displaystyle u_{\star }}$ is the friction velocity which depends on the shear stress τ_w at the boundary of the flow:

with ρ the fluid density.

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