The open source CFD toolbox
atmNutUWallFunction

# Properties

• The atmNutUWallFunction boundary condition provides a wall constraint on the turbulent viscosity, i.e. nut, based on velocity, i.e. U, for atmospheric boundary layer modelling.
• The atmNutUWallFunction condition inherits the traits of the nutUWallFunction boundary condition.

nut    | Turbulent viscosity              [m2/s]
U      | Velocity                         [m/s]


# Model equations

The boundary condition expression is:

$\nu_{t_w} = \frac{(u^*)^2 y}{max( u_p , 10^{-6} )} - \nu_w$

with

$u^* = \frac{ u_p \kappa}{\ln \left(max(E^\prime, 1 + 10^{-4}) \right)}$

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

$u_p = | \u_p - (\u_p \cdot \vec{n}) \vec{n} |$

where

 $$\nu_{t_w}$$ = Turbulent viscosity [m2/s] $$\nu_w$$ = Kinematic viscosity of fluid in the wall cell [m2/s] $$y$$ = Ground-normal distance [m] $$\kappa$$ = von Kármán constant [-] $$u^*$$ = Friction velocity [m/s] $$z_0$$ = Surface roughness length [m] $$u_p$$ = Magnitude of modified near-ground velocity field [m/s] $$\vec{n}$$ = Patch normal vector [m]

# Usage

Example of the boundary condition specification:

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

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

// Optional entries (unmodifiable)
boundNut        true;

// Optional (inherited) entries
kappa           0.41;
}


where the entries mean:

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

The inherited entries are elaborated in:

• nutUWallFunction
• PatchFunction1

# Further information

Source code

History

• Introduced in version v2006