fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, the von Kármán constant (or Kármán's constant), named for

Theodore von Kármán Theodore von Kármán ( hu, ( szőllőskislaki) Kármán Tódor ; born Tivadar Mihály Kármán; 11 May 18816 May 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronaut ...

, is a

dimensionless A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

constant involved in the

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

ic 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 In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. C ...

. The equation for such

boundary layer In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condi ...

flow profiles is: :

u=\frac\ln\frac,

where ''u'' is the mean

flow velocity In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...

at height ''z'' above the boundary. The roughness height (also known as

roughness length Roughness length (z_0) is a parameter of some vertical wind profile equations that model the horizontal mean wind speed near the ground. In the log wind profile, it is equivalent to the height at which the wind speed theoretically becomes zero in ...

) ''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 Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a veloci ...

which depends on the

shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...

''τ_w'' at the boundary of the flow: :

u_\star = \sqrt,

with ''ρ'' the fluid

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

. The Kármán constant is often used in

turbulence modeling Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow o ...

, for instance in boundary-layer

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...

to calculate

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

es of

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

, heat and moisture from the atmosphere to the land surface. It is considered to be a universal (''κ'' ≈ 0.40). Gaudio, Miglio and

Dey Dey (Arabic: داي), from the Turkish honorific title ''dayı'', literally meaning uncle, was the title given to the rulers of the Regency of Algiers (Algeria), Tripoli,Bertarelli (1929), p. 203. and Tunis under the Ottoman Empire from 1671 o ...

argued that the Kármán constant is however nonuniversal in flows over mobile sediment beds. In recent years the von Kármán constant has been subject to periodic scrutiny. Reviews (Foken, 2006; Hogstrom, 1988; Hogstrom, 1996) report values of ''κ'' between 0.35 and 0.42. The overall conclusion of over 18 studies is that ''κ'' is constant, close to 0.40.

References

*Bonan, G. B. (2005). ''"Land Surface Model (LSM 1.0) for Ecological, Hydrological, Atmospheric Studies. Model product"''. Available on-lin

from Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, Tennessee, U.S.A. *Foken T. (2006). "50 years of the Monin-Obukhov similarity theory". ''Boundary-Layer Meteorology'', Vol. 119, 431-447. *Gaudio, R. Miglio, R. and Dey, S. (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 *Hogstrom U (1996). "Review of some basic characteristics of the atmospheric surface layer". ''Boundary-Layer Meteorology'', Vol. 78, 215-246. *Hogstrom U (1988). "Non-dimensional wind and temperature profiles in the atmospheric surface layer-a re-evaluation". ''Boundary Layer Meteorology'', Vol. 42, 55-78.

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 {{DEFAULTSORT:Von Karman constant Boundary layer meteorology Turbulence

See also

References

External links