Effect of atmospheric boundary layer top andcapping inversion properties on mean wind profilesRoberto Alessio Cersosimo

DTU Wind Energy, Technical University of Denmark

Outline

• Conditionally neutral ABL

• Dimensional analysis – Heat flux

• Dimensional Analysis – Speed gradient

• B-law – top down similarity

• Conclusions

2 2 October 2017

DTU Wind Energy, Technical University of Denmark

The conditionally boundary layer

• Surface heat flux: neutral, stableand unstable.

• The conditionally neutral ABL ischaracterized by a null heat flux atthe surface. Buoyancy effects are due to the presence of a positive gradient of potential temperature in the free stream flow whichestablishes a downwards heat fluxinto the ABL.

3 2 October 2017

Buoyancy effects

DTU Wind Energy, Technical University of Denmark4 2 October 2017

Why bother?

DTU Wind Energy, Technical University of Denmark5 2 October 2017

Buoyancy effectsMean speed profiles

HIGH WIND, WEAK INVERSION

DTU Wind Energy, Technical University of Denmark6 2 October 2017

Buoyancy effectsMean speed profiles

LOW WIND, STRONG INVERSION

DTU Wind Energy, Technical University of Denmark

Dimensional Analysis – Heat flux

7 2 October 2017

DTU Wind Energy, Technical University of Denmark

Dimensional analysis – Heat flux

• Considering the dimensional n=5 parameters and m=4 dimensions [kg, m, s, K]:

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• Vertical coordinate:

• Air density:

• Heat flux:

• Surface stress:

• Stregth of the inversion:

Buckingham ϖ theorem

DTU Wind Energy, Technical University of Denmark

Dimensional analysis – Heat flux

9 2 October 2017

Final expression

DTU Wind Energy, Technical University of Denmark

Dimensional Analysis – Speed Gradient

10 2 October 2017

DTU Wind Energy, Technical University of Denmark

• Considering the dimensional n=6 parameters and m=4 dimensions [kg, m, s, K]:

Dimensional analysis – Speed gradient

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• Vertical coordinate:

• Air density: • Heat flux:

• Buoyancy parameter: • Speed gradient:

• Surface stress:

Buckingham ϖ theorem

DTU Wind Energy, Technical University of Denmark

B-Law

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DTU Wind Energy, Technical University of Denmark

• Using the previous expression for the heat flux in

B-Law

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B: a new length scale

DTU Wind Energy, Technical University of Denmark

B-Law

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DTU Wind Energy, Technical University of Denmark

• Using dimensional analysis it is possible to express with a good degree of accuracy the heat flux profile by the product of constant surface and ABL-top parameters and the vertical coordinate z.

• It is also possible to obtain an equation for the mean speed profile that depends on a universal function and a length scales which again depends only on surface and ABL-top parameters.

15 2 October 2017

Conclusions