atmNutWallFunction

- The
`atmNutWallFunction`

boundary condition provides a wall constraint on the turbulent viscosity, i.e.`nut`

, based on the turbulent kinetic energy, i.e.`k`

, and velocity, i.e.`U`

, for atmospheric boundary layer modelling. - The
`atmNutWallFunction`

condition inherits the traits of the`nutkWallFunction`

boundary condition.

Required fields:

nut | Turbulent viscosity [m2/s] k | Turbulent kinetic energy [m2/s2]

The boundary condition expression is (([63], Eq. 6-7), ([71], Eq. 7), ([80], Eq. 25)):

\[ \nu_{t_w} = max(\nu_{t_w}^\prime, 0) \]

with

\[ \nu_{t_w}^\prime = \frac{ \tau_w y}{max( u_p, \zeta )} - \nu_w \]

\[ \tau_w = {u^*_{u_p}} {u^*_k} \]

\[ u^*_{u_p} = \frac{\kappa u_p }{\ln \left( max (E^\prime, 1 + \zeta) \right)} \]

\[ E^\prime = \frac{y + z_0}{z_0 + z_{0_{min}} } \]

\[ u^*_k = C_{\mu}^{1/4} \sqrt{k} \]

where

\( \tau_w \) | = | Characteristic wall shear stress [m2/s2] |

\( u^*_{u_p} \) | = | Local friction velocity based on near-ground velocity [m/s] |

\( u^*_k \) | = | Local friction velocity based on near-ground k [m/s] |

\( \kappa \) | = | von Kármán constant [-] |

\( u_p \) | = | Magnitude of near-ground velocity field [m/s] |

\( y \) | = | Ground-normal coordinate [m] |

\( z_0 \) | = | Surface roughness length [m] |

\( z_{0_{min}} \) | = | Minimum surface roughness length [m] |

\( C_\mu \) | = | Empirical model constant [-] |

\( k \) | = | Turbulent kinetic energy [m2/s2] |

\( \zeta \) | = | Small value to prevent floating point exceptions [-] |

Example of the boundary condition specification:

<patchName> { // Mandatory entries (unmodifiable) type atmNutWallFunction; z0Min 0.001; // Mandatory entries (runtime modifiable) z0 uniform 0.001; // Optional (inherited) entries kappa 0.41; }

where the entries mean:

Property | Description | Type | Required | Default |
---|---|---|---|---|

type | Type name: atmNutWallFunction | word | yes | - |

z0 | Surface roughness length [m] | PatchFunction1<scalar> | yes | - |

z0Min | Minimum surface roughness length [m] | scalar | yes | - |

kappa | von Kármán constant | scalar | no | 0.41 |

The inherited entries are elaborated in:

- nutkWallFunction
- PatchFunction1

Source code

History

- Introduced in version v2006