ObukhovLength

Description

The ObukhovLength function object computes the Obukhov length field and associated friction velocity field.

When scaled by the ground-normal height, i.e. z, the Obukhov length becomes a dimensionless stability parameter, i.e. z/L, for atmospheric boundary layer modelling, expressing the relative roles of buoyancy and shear in the production and dissipation of turbulent kinetic energy.

The model expressions (56, Eq. 26):

$$u^* = \sqrt{ \max \left(\nu_t \sqrt{| \grad{\u} + \grad{\u}^T |^2}, \zeta \right)}$$ $$L_o = - \frac{(u^*)^3}{ {sign}(B) \kappa \max (|B|, \zeta)}$$

with

$$B = \alpha_t \beta \frac{\grad{T} \cdot \vec{g}}{\rho}$$

where:

$u^*$ : Friction velocity, [m/s]

$\nu_t$ : Turbulent viscosity, [m2/s]

$\u$ : Velocity, [m/s]

$L_o$ : Obukhov length, [m]

$B$ : Buoyancy production term, [m2/s3]

$\alpha_t$ : Kinematic turbulent thermal conductivity, [m2/s]/[kg/m/s]

$\rho$ : Density of fluid, [kg/m3]

$\beta$ : Thermal expansion coefficient, [1/K]

$T$ : Temperature, [K]

$\vec{g}$ : Gravitational acceleration, [m/s2]

$\zeta$ : A very small number to avoid floating point exceptions, [-]

Required fields:

U           | Velocity                                 [m/s]
T           | Temperature                              [K]
nut         | Turbulent viscosity                      [m2/s]
alphat      | Kinematic turbulent thermal conductivity [m2/s]/[kg/m/s]
g           | Gravitational acceleration               [m/s2]

Operands

Operand	Type	Location
input	-	-
output file	-	-
output field 1	volScalarField	$FOAM_CASE/<time>/<ObukhovLength>
output field 2	volScalarField	$FOAM_CASE/<time>/<Ustar>

Usage

Example of the ObukhovLength function object by using functions sub-dictionary in system/controlDict file:

ObukhovLength1
{
    // Mandatory entries (unmodifiable)
    type            ObukhovLength;
    libs            (fieldFunctionObjects);

    // Optional entries (runtime modifiable)
    U               U;
    result1         ObukhovLength;
    result2         Ustar;
    rhoRef          1.0;
    kappa           0.4;
    beta            3e-3;

    // Optional (inherited) entries
    region          region0;
    enabled         true;
    log             true;
    timeStart       0;
    timeEnd         1000;
    executeControl  timeStep;
    executeInterval 1;
    writeControl    timeStep;
    writeInterval   1;
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: ObukhovLength	word	yes	-
libs	Library name: fieldFunctionObjects	word	yes	-
U	Name of the velocity field	word	no	U
result1	Name of the output field for ObukhovLength	word	no	ObukhovLength
result2	Name of the output field for Ustar	word	no	Ustar
rhoRef	Reference density (to convert from kinematic to static pressure)	scalar	no	1.0
kappa	von Kármán constant	scalar	no	0.40
beta	Thermal expansion coefficient	scalar	no	3e-3

The inherited entries are elaborated in:

• functionObject

Example by using the postProcess -func utility:

postProcess -func "ObukhovLength(<UField>)"

Further information

Tutorial:

• atmForestStability

Source code:

• ObukhovLength

API:

• Foam::functionObjects::ObukhovLength

History: Introduced in version v2006