The open source CFD toolbox
atmNutWallFunction

# Properties

• 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.

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


# Model equations

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 [-]

# Usage

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

# Further information

Source code

History

• Introduced in version v2006