Commit e9ea44e4 authored by Olivier's avatar Olivier

Chapter 8: Fix definition of epsilon, which was much too imprecise

parent 05be1512
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......@@ -170,11 +170,13 @@
To convince oneself that the parameters are related, one may insert $I$ (eq.~\ref{eq_i}) into eq.~\ref{eq_k} to show that $k = 3/2 \ \overline{V}^2 I^2$.
We define the \vocab{turbulent dissipation rate} $\epsilon$ as the time rate change of $k$:
We define the \vocab{turbulent dissipation rate} $\epsilon$ as the rate of turbulent kinetic energy dissipation to heat. When no turbulence is produced, so that turbulence is simply left to decay, then $\epsilon$ is the time rate change of $k$:
\begin{IEEEeqnarray}{rCl}
\epsilon &\equiv& -\partialtimederivative{k}
\epsilon &=& -\partialtimederivative{k}
\end{IEEEeqnarray}
\begin{equationterms}
\item when no new turbulence is produced.
\end{equationterms}
The dissipation rate is measured in $\si{\watt\per\kilogram}$ and represents the local amount of turbulent kinetic energy that is currently being converted to heat through viscosity.
Through dimensional analysis, Kolmogorov and his peers showed that in homogeneous, fully-developed and isotropic turbulence, the size, characteristic velocity, and characteristic time scale of the smallest eddies could be related to the dissipation rate with the relationships:
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