## 1. The Mann uniform shear turbulence model

The IEC Turbulence Simulator is an implementation of the Mann method recommended in IEC61400-1 Ed. 3. It is distributed with Wasp Engineering and, since February 2009, it is also available as a separate tool without a license. The IEC Turbulence Simulator simulates standard turbulence over flat uniform terrain. The simulated turbulence can be used as input to aero-elastic turbine simulators, which in turn can calculate fatigue loads, e.g. as part of the requirements for obtaining an IEC turbine certificate.

The method is based on rapid-distortion theory. For the present application, atmospheric turbulence is modelled as an initially isotropic spectral tensor deformed by the shear of the mean wind profile.

### 1.1. Direct input

The following input arguments are required to execute the turbulence generator:

 $\Delta x$,$\Delta y$,$\Delta z$ Distance between grid point in X-direction (wind direction), Y-direction (horizontal and normal to wind direction) and Z-direction (vertical) $Nx$,$Ny$,$Nz$ Number of grid points in X, Y and Z direction (power of 2) $\gamma=3.9$ Gamma is the non-dimensional shear distortion parameter $l$ Length Scale parameter, normally in the range $0.7\cdot\Lambda_1$ to $0.8\cdot\Lambda_1$ where $\Lambda_1$ is the longitudinal turbulence scale parameter which for a hub height $z$ is given by $\alpha\epsilon^{2/3}$ AlphaEpsilon is a parameter in Mann’s model. For best agreement with IEC61400-1 it can be calculated according to where $\sigma_{iso}^2$ is the un-sheared, isotropic variance. The relation between $\sigma_{iso}$ and the standard deviation of the wind velocity in the mean wind direction. $\sigma_{1}$ is to be taken as: $\sigma_{iso}=0.55\cdot\sigma_{1}$ HF Compensation If HF compensation is applied, point velocity represents local anemometer measurements. Else, point velocity represents average in grid box.

The necessary input data are described in IEC61400-1, third edition, ch. 6.3 Wind conditions and Annex B - Turbulence models.

Note that

1. The duration [$T$] of the generated turbulent wind is related to the point distance in X, number of points in X and the Mean Wind Speed at hub [$U$] as 2. The dimensions of the wind box, e.g. the length, width and height are given by
table(borderlessWhite).
| $Lx=Nx\cdot \Delta x$|
| $Ly=Ny\cdot \Delta y$|
| $Lz=Nz\cdot \Delta z$|

### 1.2. Derived input

The select box Derived input may be used for easier input specification. In this select box the following applies:

1. The relation between the Length Scale parameter [$l$] and the Longitudinal Turbulence Scale Parameter [$\Lambda_{1}$] is given by the Length Factor [$f_{L}$], i.e. $l=f_{L}\cdot \Lambda_{1}$

2. The length of the generated wind box [$Lx$] is calculated based on Wind Series Duration [$T$] and Mean Wind Speed [$U$] by the equation

$Lx=T\cdot U$

3. The un-sheared, isotropic variance is calculated according to 4. The AlphaEpsilon parameter is thus calculated according to ### 1.3. Scaling of generated wind field

The specified Turbulence Intensity [$TI$] is used to scale the generated turbulence series. The scale factor is established based on the averaged standard deviation of the wind series in the X direction of the 4 grid points closest to the turbulence box center (at the hub) and the specified standard deviation: $\sigma_{1}=TI\cdot U$. All wind components are then scaled using the established scale factor.