deletions | additions       diff --git a/subsection_Local_Analysis_Many_of__.tex b/subsection_Local_Analysis_Many_of__.tex  index d3e2617..104c74a 100644  --- a/subsection_Local_Analysis_Many_of__.tex  +++ b/subsection_Local_Analysis_Many_of__.tex 
...
\end{equation}  In other words, gravity waves will be strongly modified when the local Alfven velocity is comparable to the radial component of the gravity wave group velocity. Another way of expressing this is that gravity waves will be altered when $\omega \lesssim \omega_{MG}$, where the magneto-gravity wave frequency is defined as  \begin{equation}  \label{eqn:maggrav} \label{eqn:maggrav2}  \omega_{MG} = \sqrt{2 v_A N k_\perp}.  \end{equation}