An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles

Parmhed, Oskar; Kos, Igor; Grisogono, Branko

doi:10.1007/s10546-004-5940-0

Cited by 21 publications

(13 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Within the WKB(J) theory (e.g. Bender and Orszag, 1978;Grisogono, 1995;Oerlemans, 2001a, 2001b;Parmhed et al, 2005), the angle α 0 will be shown to largely concur with that from SH09 and van Ulden and Holtslag (1985). To reword, the angle α 0 ∼ 35 • will be estimated analytically in this study.…”

Section: Introductionmentioning

confidence: 65%

“…(3) allows for gradual variations of the previously introduced I(z) = {f /(2K)} 1/2 z by simply integrating K(z) vertically (Grisogono, 1995). This is the essence of the WKB method for boundary-layer flows (Bender and Orszag, 1978;Berger and Grisogono, 1998;Parmhed et al, 2005). Now, various reasonably smooth profiles may be deployed in Eq.…”

Section: Gradually Varying Eddy Diffusivity K(z)mentioning

confidence: 99%

See 1 more Smart Citation

The angle of the near‐surface wind‐turning in weakly stable boundary layers

Grisogono

2011

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

The angle between the near-surface and geostrophic wind vector, α 0 , is discussed in the light of existing and improved Ekman theory and, on the other hand, recently obtained numerical results corroborated by some experimental data, both obtained by other researchers. The latter results for weakly stably stratified boundary layers, also based on large-eddy simulation (LES) data, give an angle that is about α 0 ≈ 35 • . If the Ekman theory is applied slightly above the horizontal surface z > 0, for almost any gradually varying eddy diffusivity K(z), which is more realistic than K = const used at z = 0 in the classic theory, a closer analytic value to α 0 can be provided (32 • to 37 • ) than that in the classic Ekman theory (45 • ). Alternatively, and without deploying the refined Ekman surface layer theory already suggested here, one may a priori use the previously confirmed result, α 0 ≈ 35 • , together with any smooth K(z) in order to find the corresponding surface layer depth. These results, bridging the gap between the existing theory toward fine numerical and limited experimental data, may aid further analyses of weakly stably stratified boundary layers. The information about the angle α 0 should be considered in NWP, air-pollution, wind-energy and climate models; otherwise, many important boundary-layer features will remain modelled inadequately.

show abstract

Section: Introductionmentioning

confidence: 65%

Section: Gradually Varying Eddy Diffusivity K(z)mentioning

confidence: 99%

The angle of the near‐surface wind‐turning in weakly stable boundary layers

Grisogono

2011

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, this solution is unphysical both at the surface and at the interface with the free tropospheric flow, and several alternative analytical solutions with more realistic functions for the eddy coefficient can be found in the literature (e.g. Nieuwstadt 1985;Grisogono and Oerlemans 2001;Tan 2001;Parmhed et al 2005).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Model Results for the Turning of the Wind and Related Momentum Fluxes in the Stable Boundary Layer

Svensson

Holtslag

2009

Boundary-Layer Meteorol

View full text Add to dashboard Cite

The turning of wind with height and the related cross-isobaric (ageostrophic) flow in the thermally stable stratified boundary layer is analysed from a variety of model results acquired in the first Global Energy and Water Cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS1). From the governing equations in this particular simple case it becomes clear that the cross-isobaric flow is solely determined by the surface turbulent stress in the direction of the geostrophic wind for the quasi-steady state conditions under consideration. Most models indeed seem to approach this relationship but for very different absolute values. Because turbulence closures used in operational models typically tend to give too deep a boundary layer, the integrated total cross-isobaric mass flux is up to three times that given by research numerical models and large-eddy simulation. In addition, the angle between the surface and the geostrophic wind is typically too low, which has important implications for the representation of the larger-scale flow. It appears that some models provide inconsistent results for the surface angle and the momentum flux profile, and when the results from these models are removed from the analysis, the remaining ten models do show a unique relationship between the boundary-layer depth and the surface angle, consistent with the theory given. The present results also imply that it is beneficial to locate the first model level rather close to the surface for a proper representation of the turning of wind with height in the stable boundary layer.

show abstract

“…Of course, other choices are possible depending on specific cases addressed. Further details on estimating K max and h can be found in Grisogono and Oerlemans (2002) and Parmhed et al (2004); Parmhed et al (2005).…”

Section: The Wkb Solutionsmentioning

confidence: 99%

“…Additional remarks on how to estimate the input parameters for this Ekman-Prandtl model type with K(z) can be found in Parmhed et al (2004); Parmhed et al (2005). The new analytical solutions (U, V, θ) WKB , (16), (17) and (18) are not named "asymptotic", which usually holds for the WKB solutions, only because we weakly decoupled (2) so that V WKB does not feed back to the original system (1)-(3).…”

Section: Comparison With the Numerical And Constant-k Solutionsmentioning

confidence: 99%

Katabatic flow with Coriolis effect and gradually varying eddy diffusivity

Kavčič

Grisogono

2007

Boundary-Layer Meteorol

Self Cite

View full text Add to dashboard Cite

Katabatic flows over high-latitude long glaciers experience the Coriolis force. A sloped atmospheric boundary-layer (ABL) flow is addressed which partly diffuses upwards, and hence, becomes progressively less local. We present the analytical and numerical solutions for (U, V, θ) depending on (z, t) in the katabatic flow, where U and V are the downslope and cross-slope wind components and θ is the potential temperature perturbation. A Prandtl model that accounts for the Coriolis effect, via f , does not approach a steady state, because V diffuses upwards in time; the rest, i.e., (U, θ), are similar to that in the classic Prandtl model. The V component behaves in a similar manner as the solution to the 1st Stokes (but inhomogeneous) problem. A WKB approach to the problem of the sloped ABL winds is outlined in the light of a modified Ekman-Prandtl model with gradually varying eddy diffusivity K(z). Ideas for parameterizing these high-latitude persistent flows in climate models are revealed.

show abstract

An Improved Ekman Layer Approximation for Smooth Eddy Diffusivity Profiles

Cited by 21 publications

References 14 publications

The angle of the near‐surface wind‐turning in weakly stable boundary layers

The angle of the near‐surface wind‐turning in weakly stable boundary layers

Analysis of Model Results for the Turning of the Wind and Related Momentum Fluxes in the Stable Boundary Layer

Katabatic flow with Coriolis effect and gradually varying eddy diffusivity

Contact Info

Product

Resources

About