Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

Freedman, A.; Jacobson, Bertil

doi:10.1023/a:1012715626037

Cited by 38 publications

(8 citation statements)

References 22 publications

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“…250 N. Afzal Coleman (1999), Shingai and Kawamura (2004) and laboratory data of Caldwell et al (1972); b the matching derivative function χ∂u + /∂χ versus χ for the mesolayer variables from DNS data of Spalart et al (2008) The geostrophic drag and cross-isobaric angle data tabulated in Tables I-IV of Hess and Garratt (2002) from many sources, laboratory data of Caldwell et al (1972) and Howroyd and Slawson (1975), DNS data of Spalart et al (2008); Shingai and Kawamura (2004); Coleman (1999); Coleman et al (1990) and Lin et al (1997) and predictions by E-e model of Freedman and Jacobson (2002) are considered. The geostrophic velocity component U g /u * Fig.…”

Section: Resultsmentioning

confidence: 99%

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

Afzal

2009

Boundary-Layer Meteorol

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The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wallwake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10 5 . The data show low Rossby number effects for Ro < 10 5 and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10 3 .Keywords Clauser's outer layer · Intermediate layer · Izakson-Millikan-Kolmogorov hypothesis · Mesolayer effect · Neutral barotropic planetary boundary layer · Rossby number effects IntroductionAtmospheric (planetary) turbulent boundary-layer descriptions have been presented by Hess and Garratt (2002) showing the influence of geostrophic wind. Further, Garratt and Hess (2002, p. 256, Fig. 2) compared the geostrophic velocity profile observations (including

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Section: Resultsmentioning

confidence: 99%

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

Afzal

2009

Boundary-Layer Meteorol

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“…The geostrophic-drag predictions have been analysed from extensive data from many sources: the laboratory data of Caldwell et al (1972) and Howard and Slawson (1975); the DNS data of Shingai and Kawamura (2004), Coleman (1999), Coleman et al (2005), Coleman et al (1990) and Lin et al (1997); and the turbulence model of Freedman and Jacobson (2002): see Hess and Garratt (2002, tables I, II, IV). Figure 9(a) shows the components of the geostrophic drag U g /u * plotted against the Rossby number Ro * , from the above data, on a semi-log plot.…”

Section: Resultsmentioning

confidence: 99%

Power‐law velocity profile in a turbulent Ekman layer on a transitional rough surface

Afzal

2008

Quart J Royal Meteoro Soc

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A two-layer asymptotic theory of mean momentum in a turbulent Ekman layer without any closure model (such as eddy viscosity, mixing length, or k − ) for large Rossby numbers is proposed. The flow in the inner wall layer and the outer wake layer are matched, using the Izakson-Millikan-Kolmogorov hypothesis; this leads to an open functional equation. Another open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation; this admits two functional solutions, with power-law and log-law velocity profiles. The envelope of the geostrophic-drag power law leads to the log law, and determines the power-law index and prefactor as a function of the surface Rossby number or the drag coefficient. The log laws and power laws for velocity and friction velocity, including the power-law constants, are universal, and independent of the wall roughness. This universality is well supported by extensive experimental and laboratory data. In traditional smooth-wall variables, there is no universality of scalings, and different expressions are needed for different types of roughness. Approximate solutions of the power-law geostrophic drag and cross-isobaric angle are also obtained. The power-law geostrophic-drag solution for each prescribed value of the power-law index is valid for a limited domain of Rossby numbers. Copyright  2008 Royal Meteorological Society KEY WORDS power-law and log-law velocity profiles; Rossby-number similarity theory; neutral barotropic planetary boundary layer; Izakson-Millikan-Kolmogorov hypothesis

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“…Predicted turbulent length scale distributions as a function of distance from the ground, for the Cabauw (G ¼ 10 m s À1 ) neutral Ekman-layer data, see Van Ulden and Wieringa (1996). Recently, Freedman and Jacobson (2002) have derived analytical solutions of the coupled k and e equations for the case of steady balance between transport and dissipation terms, which is the dominant balance just below the boundary-layer top. They have provided analytical conditions for the point where the turbulent length scale profiles made a transition from decreasing to increasing values with height.…”

Section: Fully-developed Channel Flowmentioning

confidence: 99%

“…Many efforts have been made since then to remove the mentioned deficiency of the standard k-e model; see Detering and Etling (1985), Duynkerke (1988), Andren (1991), Andren and Moeng (1993), Apsley and Castro (1997), Xu and Taylor (1997) and Freedman and Jacobson (2002).…”

Section: Introductionmentioning

confidence: 99%

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

Venetsanos

Bartzis

Andronopoulos

2004

Boundary-Layer Meteorol

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A new algebraic turbulent length scale model is developed, based on previous oneequation turbulence modelling experience in atmospheric flow and dispersion calculations. The model is applied to the neutral Ekman layer, as well as to fully-developed pipe and channel flows. For the pipe and channel flows examined the present model results can be considered as nearly equivalent to the results obtained using the standard k-e model. For the neutral Ekman layer, the model predicts satisfactorily the near-neutral Cabauw friction velocities and a dependence of the drag coefficient versus Rossby number very close to that derived from published (G. N. Coleman) direct numerical simulations. The model underestimates the Cabauw cross-isobaric angles, but to a less degree than the cross-isobar angle versus Rossby dependence derived from the Coleman simulation. Finally, for the Cabauw data, with a geostrophic wind magnitude of 10 m s À1 , the model predicts an eddy diffusivity distribution in good agreement with semi-empirical distributions used in current operational practice.

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Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

Cited by 38 publications

References 22 publications

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

Power‐law velocity profile in a turbulent Ekman layer on a transitional rough surface

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

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