## Properties🔗

• The atmLengthScaleTurbSource applies sources on either epsilon or omega to correct mixing-length scale estimations for atmospheric boundary layer modelling.
• The atmLengthScaleTurbSource can be applied on epsilon or omega based RAS turbulence models.
• The atmLengthScaleTurbSource inherits the traits of the fvOption, and cellSetOption.

Corrections applied to either of the below, if exist:

epsilon
Turbulent kinetic energy dissipation rate [m$$^2$$/s$$^3$$]
omega
Specific dissipation rate [1/s]

epsilon
Turbulent kinetic energy dissipation rate [m$$^2$$/s$$^3$$]
omega
Specific dissipation rate [1/s]

## Model equations🔗

### Turbulent kinetic energy dissipation rate🔗

The model expression for epsilon:

$S_p = \alpha \rho C_1^* \frac{G_o}{\nu} C_\mu k_o$

with (, Eq. 16 wherein the exponentiation n is not present. n is an ad-hoc implementation):

$C_1^* = (C_2 - C_1) \left( \frac{L}{L_{max}} \right)^n$

Mixing-length scale estimation (, Eq. 10.37 & p. 374):

$L = C_\mu^{3/4} \frac{k_o^{3/2}}{\epsilon_o}$

### Specific dissipation rate🔗

The model expression for omega:

$S_p = \alpha \rho \gamma^* \frac{G_o}{\nu}$

with (, Eq. 3.34):

$\gamma^* = \left( \gamma - \beta \right) \left( \frac{L}{L_{max}} \right)^n$

Mixing-length scale estimation (, Eq. 3.20):

$L = \frac{\sqrt{k}}{C_\mu^{1/4} \omega_o}$

Where:

$$S_p$$
Source term without boundary conditions
$$\epsilon_o$$
Previous-iteration epsilon [m2/s3]
$$\omega_o$$
Previous-iteration omega [1/s]
$$k_o$$
Previous-iteration k [m2/s2]
$$G_o$$
Previous-iteration k-production contribution [m2/s3]
$$C_1$$
Model constant (epsilon-based models) [-]
$$C_2$$
Model constant (epsilon-based models) [-]
$$C_1^*$$
Modified model constant field (epsilon-based models) [-]
$$C_\mu$$
Empirical model constant [-]
$$\gamma$$
Model constant (omega-based models) [-]
$$\beta$$
Model constant (omega-based models) [-]
$$\gamma^*$$
Modified model constant field (omega-based models) [-]
$$\nu$$
Kinematic viscosity of fluid [m2/s]
$$L$$
Mixing-length scale [m]
$$L_{max}$$
Maximum mixing-length scale [m]
$$\alpha$$
Phase fraction in multiphase computations, otherwise equals to 1
$$\rho$$
Fluid density in compressible computations, otherwise equals to 1

## Usage🔗

Example of the fvOptions specification using constant/fvOptions file:

atmLengthScaleTurbSource1
{
// Mandatory entries (unmodifiable)
type                  atmLengthScaleTurbSource;

atmLengthScaleTurbSourceCoeffs
{
// Mandatory (inherited) entries (unmodifiable)
selectionMode    all;

// Optional entries (unmodifiable)
rho              rho;
Lmax             41.575;
n                3.0;
}

// Optional (inherited) entries
...
}


where the entries mean:

Property Description Type Required Default
type Type name: atmLengthScaleTurbSource word yes -
rho Name of density field word no rho
Lmax Maximum mixing-length scale scalar no 41.575
n Mixing-length scale exponent scalar no 3.0

The inherited entries are elaborated in:

## Further information🔗

Tutorials

Source code

History:

• Introduced in version v2006