The open source CFD toolbox
atmNutkWallFunction

Properties

• The atmNutkWallFunction boundary condition provides a wall constraint on the turbulent viscosity, i.e. nut, based on the turbulent kinetic energy, i.e. k, for atmospheric boundary layer modelling.
• The atmNutkWallFunction condition inherits the traits of the nutkWallFunction boundary condition.

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


Model equations

The boundary condition expression is (based on ([24], Eq. 5)):

$\nu_{t_w} = \nu_w \left( \frac{y^+ \kappa}{\ln \left( max (E^\prime, 1 + 10^{-4}) \right) } - 1 \right)$

with

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

$y^+ = \frac{u^* y}{\nu_w}$

$E^\prime = \frac{y + z_0}{z_0}$

where

 $$\nu_{t_w}$$ = Turbulent viscosity [m2/s] $$\nu_w$$ = Kinematic viscosity of fluid near wall [m2/s] $$y^+$$ = Wall-normal distance in wall units [-] $$\kappa$$ = von Kármán constant [-] $$u^*$$ = Friction velocity [m/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            atmNutkWallFunction;

// Mandatory entries (runtime modifiable)
z0              uniform 0.001;

// Optional entries (unmodifiable)
boundNut        false;

// Optional (inherited) entries
Cmu             0.09;
kappa           0.41;
}


where the entries mean:

Property Description Type Required Default
type Type name: atmNutkWallFunction word yes -
z0 Surface roughness length [m] PatchFunction1<scalar> yes -
boundNut Flag: zero-bound nut near wall bool no false
Cmu Empirical model constant scalar no 0.09
kappa von Kármán constant scalar no 0.41

The inherited entries are elaborated in:

• nutkWallFunction
• PatchFunction1

Further information

Tutorial:

Source code

History

• Introduced in version v2006
• Previously known as:
• nutkAtmRoughWallFunction : 2.1.1