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atmAlphatkWallFunction

# 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.

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