# Stable Benchmark¶

This exercise will reveal how well different models perform under stable conditions, often encountered at nighttime and associated with high shear and consistent winds.

This benchmark focuses on “Wake Evolution under Stable Atmospheric Conditions”. The validation focuses on the mean characteristics of a single wake as it propagates in a stable nocturnal boundary layer. The objective of this exercise is to evaluate the ability of various models to simulate the downstream evolution of a single wake under these conditions, which are typically difficult to model since the turbulence is of small scale, weak, and often intermittent.

This benchmark welcomes all models. Models which cannot model stability are encouraged to simulate low-turbulence, high-shear neutral conditions as an analogous inflow scenario and to assess the performance of this approach through the benchmark exercise. This document provides detailed, quantitative information necessary to engage in this specific SWiFT Benchmark. For general information about the SWiFT Benchmarks, see The SWiFT Benchmarks.

## The Measurements¶

Wake measurements were collected between 1 D and 5 D downstream of the rotor, and the validation focuses on mean wake characteristics at these distances. In addition, models will be cross-compared for quantities of interest for which measurements are not available.

## The Simulation¶

Participants are asked to simulate the mean wake behind a single turbine (between 1 D and 8 D) operating in a stable atmosphere under the inflow described below. Please observe the simulation guidelines for information that is common to all SWiFT benchmarks (e.g., turbine model, requested output files).

**Inflow Conditions**

The information below should be used by the benchmark participants to simulate atmospheric inflow (in the case of higher-fidelity models) or to constrain the parameters used to initialize the model (in the case of lower-fidelity models). Not all information given will necessarily be used to perform the simulations. Note that the values provided refer to the ensemble average of six 10-minute temporal averages.

Variable | Short Description | Value | Unit | Remark |

\(\langle \overline{U}_{hub} \rangle\) | Mean hub-height wind speed | 4.8 | m/s | |

\(\langle \overline{TI}_{hub} \rangle\) | Mean hub-height turbulence intensity | 3.4 | % | |

\(\langle \alpha\rangle\) | Mean wind-speed profile power-law exponent | 0.50 | - | |

\(z_0\) | Roughness length | 0.005-0.05 | m | Value obtained from the neutral benchmark measurements |

\(z_i\) | Atmospheric boundary layer height | m | No measurements available | |

\(\langle z/L \rangle\) | Stability parameter | 1.151 | - | Computed from sonic measurements at \(z=10\) m |

\(\langle u_* \rangle\) | Friction velocity | 0.08 | m/s | Computed from sonic measurements at \(z=10\) m |

\(\langle \overline{w'\theta_v'} \rangle\) | Kinematic vertical turbulent heat flux | -0.005 | K m/s | Computed from sonic measurements at \(z=10\) m |

\(\langle \theta_v \rangle_0\) | Virtual potential temperature near ground | 304.2 | K | Computed from temperature and pressure sensors at \(z=2\) m |

\(\langle \rho \rangle_{hub}\) | Air density | 1.06 | kg m-3 | Total air density, considers dry air and water vapor |

**Turbine Operation**

Please see turbine model details.