deletions | additions       diff --git a/subsection_Local_Analysis_Many_of__.tex b/subsection_Local_Analysis_Many_of__.tex  index 2673ca6..042674a 100644  --- a/subsection_Local_Analysis_Many_of__.tex  +++ b/subsection_Local_Analysis_Many_of__.tex 
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\label{eqn:magnetogravity2}  v_{A,r} \sim v_{g,r} \, .  \end{equation}  Here, we have used $\mu v_A \sim v_{A,r}$ because $k_r \gg k_\perp$ for gravity waves in the WKB limit. Therefore, the radial component of the field dominates the interaction between the magnetic field and gravity waves. Equation \ref{eqn:maagnetogravity2} \ref{eqn:magnetogravity2}  shows that gravity waves will be strongly modified when the radial component of the 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:maggrav2}  \omega_{MG} = \sqrt{2 v_{A,r} N k_\perp}.