deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index e85d7f2..02ea978 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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\label{eqn:Ewaves}  \mathcal{M} L_{\rm con} \lesssim \dot{E} \lesssim \mathcal{M}^{5/8} L_{\rm con} \, ,   \end{equation}  where $\mathcal{M}$ is the convective Mach number (defined as $v_{\rm con}/c_s$, with $c_s$ the sound speed),  and $L_{\rm con}$ is the luminosity carried by convection near the base of the convective zone. Many previous works have used the left-hand side of equation \ref{eqn:Ewaves} as an estimate for the IGW energy flux, although \cite{Lecoanet_2013} argue that a more accurate estimate may be $\dot{E} \sim \mathcal{M}^{5/8} L_{\rm con}$, which is larger by a factor of $\mathcal{M}^{-3/8}$. We consider the left-hand side of \ref{eqn:Ewaves} to be a lower limit for the wave flux, and the right-hand side to be an upper limit. For shell burning, this energy flux is dominated by waves with horizontal wave numbers and angular frequencies near $\bar{m} \sim {\rm max}(r_c/H_c,1)$, and $\bar{\omega} \sim \omega_{\rm con}$, respectively. Here, $H_c$ and $r_c$ are the pressure scale height and radial coordinate near the base of the convective zone, and we define the angular convective turnover frequency as