atmAlphatkWallFunction

Table of Contents

Properties

  • The atmAlphatkWallFunction boundary condition provides a wall constraint on the kinematic turbulent thermal conductivity, i.e. alphat, for atmospheric boundary layer modelling.
  • The condition assumes a logarithmic distribution of the potential temperature within the first cell.
  • The atmAlphatkWallFunction condition inherits the traits of the fixedValue boundary condition.

Required fields: 

alphat    | Kinematic turbulent thermal conductivity    [m2/s]

Model equations

The boundary condition expression is:

\[ \alpha_t = max (\alpha_t^\prime, 0.01) \]

with

\[ \alpha_t^\prime = \frac{u^* \kappa y}{{Pr}_t \ln \left(max(E^\prime, 1 + 10^{-4} )\right)} + \frac{\nu_w}{Pr} \]

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

\[ E^\prime = \frac{y + z_0}{z_0 + 10^{-4}} \]

where

\( \alpha_t \) = Kinematic turbulent thermal conductivity [m2/s]
\( u^* \) = Friction velocity [m/s]
\( \kappa \) = von Kármán constant [-]
\( y \) = Ground-normal height [m]
\( Pr \) = Molecular Prandtl number [-]
\( {Pr}_t \) = Turbulent Prandtl number [-]
\( \nu_w \) = Kinematic viscosity of fluid in the wall cell [m2/s]
\( C_\mu \) = Empirical model constant [-]
\( k \) = Turbulent kinetic energy [m2/s2]
\( z_0 \) = Surface roughness length [m]

Usage

Example of the boundary condition specification: 

<patchName>
{
    // Mandatory entries (unmodifiable)
    type            atmAlphatkWallFunction;

    // Mandatory entries (runtime modifiable)
    Pr              0.90;
    Prt             uniform 0.85;
    z0              uniform 0.001;

    // Optional entries (unmodifiable)
    Cmu             0.09;
    kappa           0.41;

    // Optional (inherited) entries
    value           uniform 0;
}

where the entries mean:

Property Description Type Required Default
type Type name: atmAlphatkWallFunction word yes -
Pr Molecular Prandtl number TimeFunction1<scalar> yes -
Prt Turbulent Prandtl number PatchFunction1<scalar> yes -
z0 Surface roughness length [m] PatchFunction1<scalar> yes -
Cmu Empirical model constant scalar no 0.09
kappa von Kármán constant scalar no 0.41

The inherited entries are elaborated in:

Further information

Tutorial:

Source code

History

  • Introduced in version v2006