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: