Von Kármán constant

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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 τw 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.

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References[edit]

  • 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

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