# An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes

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## Abstract

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## 1. Introduction

## 2. Large-Eddy Simulation Framework

#### 2.1. LES Governing Equations

#### 2.2. Numerical Setup

#### 2.3. LES Results

## 3. Analytical Wake Model

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Mean profiles of (

**a**) horizontal wind components, (

**b**) wind direction, and (

**c**) potential temperature of the incoming atmospheric boundary layer (ABL) flow. The top and the bottom of the rotor planes are shown with the horizontal dotted lines.

**Figure 2.**Two-dimensional field of the normalized velocity deficit in the $y-z$ planes at x/D = 3, 5, 7, and 10 downstream of the turbine obtained from the LES. The location of the turbine is marked with the white circle.

**Figure 3.**A schematic of the skewed wake at some distance downstream. Red circle is the original wake. The blue dots shows the skewed wake. The black arrows indicate the lateral component of the incoming wind.

**Figure 4.**Maximum velocity deficit with downstream distance. LES data (open red circle), and Gaussian wake model (solid black line).

**Figure 5.**Wall-normal (

**left**) and lateral (

**right**) profiles of the normalized velocity deficit ($\Delta U/{U}_{hub}$) through the turbine center at $x/D=3,5,7,10$ downstream of the turbine. LES data (open red circle), the proposed model (solid black line), and the axisymmetric wake model [15] (dashed green line).

**Figure 6.**Two-dimensional field of the normalized velocity deficit in the $y-z$ planes at $x/D=$ 3, 5, 7, and 10 downwind of the turbine obtained from the proposed model (

**top**) and the axisymmetric wake model [15] (

**bottom**). The location of the turbine is marked with the white circle.

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**MDPI and ACS Style**

Abkar, M.; Sørensen, J.N.; Porté-Agel, F.
An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes. *Energies* **2018**, *11*, 1838.
https://doi.org/10.3390/en11071838

**AMA Style**

Abkar M, Sørensen JN, Porté-Agel F.
An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes. *Energies*. 2018; 11(7):1838.
https://doi.org/10.3390/en11071838

**Chicago/Turabian Style**

Abkar, Mahdi, Jens Nørkær Sørensen, and Fernando Porté-Agel.
2018. "An Analytical Model for the Effect of Vertical Wind Veer on Wind Turbine Wakes" *Energies* 11, no. 7: 1838.
https://doi.org/10.3390/en11071838