atmEpsilonWallFunction

Table of Contents

Properties

  • The atmEpsilonWallFunction boundary condition provides a wall constraint on the turbulent kinetic energy dissipation rate, i.e. epsilon, and the turbulent kinetic energy production contribution, i.e. G, for atmospheric boundary layer modelling.
  • The atmEpsilonWallFunction condition inherits the traits of the epsilonWallFunction boundary condition.

Required fields: 

epsilon    | Turbulent kinetic energy dissipation rate    [m2/s3]

Model equations

The boundary condition expression is (([63], Eq. 8), ([59], Eq. 7)):

\[ \epsilon = \frac{w C_\mu^{3/4} k^{3/2}}{\kappa (y + z_0)} \]

when \(y^+ < y^+_{lam}\) and lowReCorrection=true:

\[ \epsilon = \frac{2.0 w k \nu }{(y + z_0)^2} \]

where

\( \epsilon \) = Turbulent kinetic energy dissipation rate [m2/s3]
\( w \) = Cell-corner weights [-]
\( C_\mu \) = Empirical model constant [-]
\( k \) = Turbulent kinetic energy [m2/s2]
\( \kappa \) = von Kármán constant [-]
\( y \) = Ground-normal height [m]
\( z_0 \) = Surface roughness length [m]
\( \nu \) = Kinematic viscosity of fluid [m2/s2]

Usage

Example of the boundary condition specification: 

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

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

    // Optional (inherited) entries
    Cmu             0.09;
    kappa           0.41;
    lowReCorrection false;
}

where the entries mean:

Property Description Type Required Default
type Type name: atmEpsilonWallFunction word yes -
z0 Surface roughness length [m] PatchFunction1<scalar> yes -
Cmu Empirical model constant scalar no 0.09
kappa von Kármán constant scalar no 0.41
lowReCorrection Flag: apply low-Re correction bool no false

The inherited entries are elaborated in:

  • epsilonWallFunction
  • PatchFunction1

Further information

Tutorial:

Source code

History

  • Introduced in version v2006