# Specific turbulence dissipation rate

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The specific turbulence dissipation, $\omega$ is the rate at which turbulence kinetic energy is converted into thermal internal energy per unit volume and time. Sometimes the specific turbulence dissipation, $\omega$, is also referred to as the mean frequency of the turbulence. This is mainly based on dimensional analysis. The SI unit of $\omega$ is $1/s$.

There is no strict mathematical definition of the specific turbulence dissipation, $\omega$ (at least none known by the author, please add one here if you know it). Instead it is most often defined implicitly using the turbulence kinetic energy, $k$, and the turbulence dissipation, $\epsilon$:

$\omega \, = \, \frac{\epsilon}{k \beta^*}$

Where $\beta^*$ is a model constant, most often set to:

$\beta^* = C_\mu = 0.09$

Please note that some models/codes instead use a different definition without the model constant:

$\omega \, = \, \frac{\epsilon}{k}$