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

parent 05be1512
 \renewcommand{\lastedityear}{2019} \renewcommand{\lasteditmonth}{06} \renewcommand{\lasteditday}{03} \renewcommand{\lasteditday}{06} \renewcommand{\numberofthischapter}{8} \renewcommand{\titleofthischapter}{\namechaptereight} ... ... @@ -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: ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment