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Boundary-Layer Meteorology

, Volume 16, Issue 2, pp 155–167 | Cite as

Theoretical studies of the parameterization of the non-neutral surface boundary layer

Part I: governing physical concepts
  • Fritz Herbet
  • Walter-Georg Panhans
Article

Abstract

The parameterization of the non-neutral atmospheric surface layer has been reexamined using the basic principles of small-scale energetics and thermodynamics. On the basis of this more complete treatment, theK-parameterization has been reformulated. It is found that the linear regression laws between fluxes and driving gradient forces of the turbulent heat and humidity exchanges in the surface layer can be derived in a much more comprehensive manner than by using the commonly used K-theory.

With respect to stationary conditions and in the context of similarity concepts, a system of algebraic equations has been formulated which provides reasonable estimates of the distributions of the dimension less rates of viscous energy dissipation as well as turbulent kinetic and thermal-diffusive energy transport as functions of the variablez/L. Quantitative calculations have been performed using the scaling height formulations of Takeuchi and Yokoyama, Prandtl, and von Kârmân as closure conditions of the equations.

Keywords

Boundary Layer Surface Layer Energy Dissipation Surface Boundary Closure Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

û = (û,\(\hat v\), ŵ)

wind speed vector

ûh = (û,\(\hat v\))

horizontal wind speed vector

ŵ

vertical wind speed

u″, u″h, w″

turbulent deviations of û, û h ŵ

ê

internal energy (per unit mass)

\(\hat k\)

eddy-kinetic energy (per unit mass)

\(\bar p\)

pressure

\(\bar \rho \), ρ

density (of the total system)

ρa

density of dry air

ρ0

characteristic density, e.g. =p0/{R a [1 + (Rν/R a − 1)mν0]T0}

\(\bar T\),T

temperature [K]

\(\bar \theta \), Θ

potential temperature [K]

\(\hat m\)ν,mν

vapor mass fraction (specific humidity)

Rν,Ra

water vapor, dry air gas constants

cpa

specific heat of dry air at constant pressure

p0

fixed pressure-value (e.g. 1000 mb)

\(\bar \pi = (\bar p/p_o )^{R_a /c_{p_a } } \)T0,mν0

temperature, humidity corresponding top0

g

earth-gravity acceleration

κ

von Kármán factor

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References

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Copyright information

© D. Reidel Publishing Company 1979

Authors and Affiliations

  • Fritz Herbet
    • 1
  • Walter-Georg Panhans
    • 2
  1. 1.Eidgenössische Technische Hochschule, Atmosphärenphysik ETHZürichSwitzerland
  2. 2.Zentralamt des Deutschen WetterdienstesOffenbachFRG

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