## Properties🔗

• The atmBuoyancyTurbSource applies sources on k and either epsilon or omega to incorporate effects of buoyancy for atmospheric boundary layer modelling.
• The atmBuoyancyTurbSource can be applied on epsilon or omega based RAS turbulence models.
• The atmBuoyancyTurbSource inherits the traits of the fvOption, and cellSetOption.

Corrections applied to:

k
Turbulent kinetic energy [m$$^2$$/s$$^2$$]

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]

k
Turbulent kinetic energy [m$$^2$$/s$$^2$$]
alphat
Kinematic turbulent thermal conductivity [m$$^2$$/s]

and either of:

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 expressions for epsilon ([2], Eq. 5, rhs-term:3):

$S_p = \alpha \rho \frac{C_3 B}{k_o} \epsilon$

with (([66], Eq. 18, rhs-term:3), ([2], Eq. 5, rhs-term:3 has a typo)):

$C_3 = (C_1 - C_2) \alpha_B + 1.0;$

and ([2], Eq. 10, with a typo of $$C_2$$ instead of using $$(C_2 - 1.0)$$):

$\alpha_B = {neg}_0 (R) (1.0 - (1.0 + \frac{C_2 - 1.0}{C_2 - C_1}) L ) + pos(R) (1.0 - L)$

Mixing-length scale estimation ([59], Eq. 10.37 & p. 374) normalised by $$L_{max}$$:

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

Gradient Richardson number ([2], Eq. 4):

$R = - \frac{B}{G_o + \zeta}$

Buoyancy production term ([2], Eq. 7):

$B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g})$

### Specific dissipation rate🔗

The model expression for omega (([33]) ([2], Eq. 5, rhs-term:3)):

$S_p = \alpha \rho \frac{C_3 B}{k_o} \omega$

with (([66], Eq. 19, rhs-term:3), ([2], Eq. 5, rhs-term:3 has a typo)):

$C_3 = (\gamma - \beta) \alpha_B;$

and ([2], Eq. 10):

$\alpha_B = {neg}_0 (R) (1.0 - (1.0 + \frac{\beta}{\beta - \gamma}) L ) + pos(R) (1.0 - L)$

Mixing-length scale estimation ([33] Eq. 3.20) normalised by $$L_{max}$$:

$L = \frac{1}{C_\mu^{1/4} L_{max}} \frac{\sqrt{k_o}}{\omega_o}$

Gradient Richardson number ([2], Eq. 4):

$R = - \frac{B}{G_o + \zeta}$

Buoyancy production term ([2], Eq. 7):

$B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g})$

### Turbulent kinetic energy🔗

The model expression for k:

$S_p = \alpha \rho \frac{B}{k_o} k$

Where:

$$S_p$$
Source term without boundary conditions
$$\epsilon$$
Turbulent kinetic energy dissipation rate (Current iteration) [m2/s3]
$$\omega$$
Specific dissipation rate (Current iteration) [1/s]
$$k$$
Turbulent kinetic energy (Current iteration) [m2/s2]
$$\epsilon_o$$
Previous-iteration epsilon [m2/s3]
$$\omega_o$$
Previous-iteration omega [1/s]
$$k_o$$
Previous-iteration k [m2/s2]
$$C_1$$
Model constant (epsilon-based models) [-]
$$C_2$$
Model constant (epsilon-based models) [-]
$$\beta$$
Model constant (omega-based models) [-]
$$\gamma$$
Model constant (omega-based models) [-]
$$C_3$$
Modified model constant field [-]
$$L$$
Normalised mixing-length scale [-]
$$L_{max}$$
Maximum mixing-length scale [m]
$$B$$
Buoyancy production term [m2/s3]
$$T_o$$
Previous-iteration temperature [K]
$$\alpha_{t_o}$$
Previous-iteration kinematic turbulent thermal conductivity [m2/s]
$$G_o$$
Previous-iteration turbulent kinetic energy production contribution [m2/s2]
$$\vec{g}$$
Gravitational field [m/s2]
$$C_\mu$$
Empirical model constant [-]
$$R$$
$$\beta_B$$
Thermal expansion coefficient [-]
$$\alpha$$
Phase fraction in multiphase computations, otherwise equals to 1
$$\rho$$
Fluid density in compressible computations, otherwise equals to 1
$$\zeta$$
Small value to prevent floating-point exceptions [-]

## Usage🔗

Example of the fvOptions specification using constant/fvOptions file:

atmBuoyancyTurbSource1
{
// Mandatory entries (unmodifiable)
type                  atmBuoyancyTurbSource;

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

// Optional (unmodifiable)
rho          rho;
Lmax         41.575;
beta         3.3e-03;
}

// Optional (inherited) entries
...
}


where the entries mean:

Property Description Type Required Default
type Type name: atmBuoyancyTurbSource word yes -
kAmb Ambient value for k scalar yes -
rho Name of density field word no rho
Lmax Maximum mixing-length scale scalar no 41.575
beta Thermal expansion coefficient scalar no 3.3e-03

The inherited entries are elaborated in:

## Further information🔗

Tutorials

Source code

History:

• Introduced in version v2006