fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

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

Theodore von Kármán Theodore von Kármán ( , May 11, 1881May 6, 1963) was a Hungarian-American mathematician, aerospace engineer, and physicist who worked in aeronautics and astronautics. He was responsible for crucial advances in aerodynamics characterizing ...

, is a

dimensionless Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...

constant involved in the

logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

ic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent

fluid flow In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

near a boundary with a

no-slip condition In fluid dynamics, the no-slip condition is a Boundary conditions in fluid dynamics, boundary condition which enforces that at a solid boundary, a viscous fluid attains zero bulk velocity. This boundary condition was first proposed by Osborne Reyno ...

. 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 Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces ...

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

''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 ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

. The Kármán constant is often used in

turbulence modeling In fluid dynamics, 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. In spite of decades of research, there is no analytical ...

, for instance in boundary-layer

meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...

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 in physics. For transport phe ...

es of

momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

, 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 (, from ) was the title given to the rulers of the regencies of Algiers, Tripolitania,Bertarelli (1929), p. 203. and Tunis under the Ottoman Empire from 1671 onwards. Twenty-nine ''deys'' held office from the establishment of the deylicate ...

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. For incompressible and frictionless ("ideal") fluids, Baumert (2013) used Kolmogorov's classical ideas on turbulence to derive ideal values of a number of relevant constants of turbulent motions, among them ''von Kármán's '' constant as

\kappa = 1/\sqrt \approx 0.399

References

*Baumert, H. Z. (2013). "Universal equations and constants of turbulent motion" Physica Scripta T155 (2013) 014001 (12pp). Online at stacks.iop.org/PhysScr/T155/014001 *Baumert H. Z., Wessling B. (2016). "On turbulence in dilatant dispersions". Physica Scripta 91(7):074003. DOI:10.1088/0031-8949/91/7/074003 *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