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Substituting equation \ref{eqn:omstarnl} back into equation \ref{eqn:emax} allows us to solve for the energy and AM flux as a function of radius due to non-linear attenuation. The result is  \begin{equation}  \label{eqn:jstarnl}  \dot{J}_* \sim \bigg[ \frac{\omega_*(r)}{\omega_c} \bigg]^{-a} \dot{J}_0 \sim {\rm min} \bigg[1 \bigg[1,  \, \, \bigg( \frac{A^2 \rho r^5 \omega_c^4}{\lambda^{3/2} N \dot{E}_0} \bigg)^{a/(a+3)} \bigg] \dot{J}_0 \, . \end{equation}  During C-shell burning, we find that radiative diffusion damps waves near the shell burning convective zone, while non-linear breaking damps waves near the center of the star. In this case, we first calculate $\omega_*$ and its corresponding energy flux $\dot{E}_*$ via equations \ref{eqn:omstar2} and \ref{eqn:spectrum}. We then substitute the value of $\dot{E}_*$ for $\dot{E}_0$ in equation \ref{eqn:omstarnl}. The appropriate value of $\omega_*$ is then $\omega_* = {\rm max} \big[ {\rm Eqn.}$ \ref{eqn:omstar2}$, {\rm Eqn.}$\ref{eqn:omstarnl}$ \big]$. The corresponding AM flux is $\dot{J}_* \sim \Big[ \frac{\omega_*(r)}{\omega_c} \Big]^{-a} \dot{J}_0$.