The atmNutWallFunction is a boundary condition that 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 governing equation of the boundary condition:

\[\tau_w = {U^*_u} {U^*_k}\]


\[{U^*_u} = \frac{\kappa U_w}{ln(z_p / z_0)}\] \[{U^*_k} = C_{\mu}^{1/4} \sqrt{k}\]


Property Description
\(\tau_w\) Wall shear stress
\(U^*_u\) Local friction velocity based on near-ground velocity
\(U^*_k\) Local friction velocity based on near-ground k
\(\kappa\) von Karman constant
\(U_w\) Near-ground velocity
\(z_p\) Vertical coordinate
\(z_0\) Surface roughness length [m]
\(C_mu\) Empirical model constant
\(k\) Turbulent kinetic energy


  • Theoretical expressions (tags:RH, SBJM, SM):

    Richards, P. J., & Hoxey, R. P. (1993). Appropriate boundary conditions for computational wind engineering models using the k-ฮต turbulence model. In Computational Wind Engineering 1 (pp. 145-153). DOI:10.1016/B978-0-444-81688-7.50018-8

    Sรธrensen, N. N., Bechmann, A., Johansen, J., Myllerup, L., Botha, P., Vinther, S., & Nielsen, B. S. (2007). Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver. In Journal of Physics: Conference series (Vol. 75, No. 1, p. 012053). DOI:10.1088/1742-6596/75/1/012053

    Sumner, J., & Masson, C. (2012). kโˆ’ฮต simulations of the neutral atmospheric boundary layer: analysis and correction of discretization errors on practical grids. International journal for numerical methods in fluids, 70(6), 724-741. DOI:10.1002/fld.2709


The condition requires entries in both the boundary and field files.

Boundary file

    type            patch;

Field file

    // Mandatory entries
    type            atmNutWallFunction;
    z0Min           <scalar>;
    z0              <PatchFunction1<scalar>>;

    // Inherited entries


Property Description Type Required Default
type Type name: atmNutWallFunction word yes -
z0Min Minimum surface roughness length [m] scalar yes -
z0 Surface roughness length [m] PatchFunction1<scalar> yes -

The inherited entries are elaborated in:

  • nutkWallFunctionFvPatchScalarField.H
  • PatchFunction1.H

Further information


  • N/A

Source code:



  • Introduced in version v2006