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\label{nl}  | k_r \xi_r | = \bigg[ \frac{\lambda^{3/2} N \dot{E} }{\rho r^5 \omega^4} \bigg]^{1/2} \sim 1 \, .  \eeq  In the absence of damping, $\dot{E}$ is a conserved quantity. Therefore, waves become more non-linear as they propagate into regions with larger $N$, lower density, or smaller radius. In our problem, the geometrical focusing (i.e., the $r$-depdendence) is the most important feature of equation \ref{nl}, \ref{eqn:nl},  and causes waves to non-linearly break as they propagate inward. Note also the $\omega^{-2}$ dependence of equation \ref{nl}, \ref{eqn:nl},  which causes low frequency waves to preferentially damp. Equation \ref{nl} \ref{eqn:nl}  entails there is a maximum energy flux that can be carried by waves of frequency $\omega$, \beq  \label{emax}  \dot{E}_{\rm max} = \frac{ A^2 \rho r^5 \omega^4}{\lambda^{3/2} N} \, ,  \eeq  for waves that non-linearly break when $|k_r \xi_r| = A \sim 1$. When the waves are highly non-linear, the waves which dominate the energy flux are those which are on the verge on breaking. To determine their frequency, we use the frequency spectrum \ref{spectrum} \ref{eqn:spectrum}  to find \beq  \label{efreq}  \dot{E}_0 \bigg( \frac{\omega}{\omega_c} \bigg)^{1-a} \sim \dot{E}_{\rm max}.  \eeq  Solving equation \ref{efreq} \ref{eqn:efreq}  yields the wave frequency which dominates energy transport, \beq  \label{omstarnl}  \omega_* \sim \omega_c \bigg[ \frac{ A^2 \rho r^5 \omega_c^4}{\lambda^{3/2} N \dot{E}_0} \bigg]^{-1/(a+3)} \, .  \eeq  We expect frequency spectra with slopes somewhere near $3 \lesssim a \lesssim 7$. Therefore the exponent in equation \ref{omstarnl} \ref{eqn:omstarnl}  is quite small, and in most cases, $\omega_*$ does not increase to values much larger than $\omega_c$. Substituting equation \ref{omstarnl} \ref{eqn:omstarnl}  back into equation \ref{emax} \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 \beq  \label{jstarnl}  \dot{J}_* \sim \bigg[ \frac{\omega_*(r)}{\omega_c} \bigg]^{-a} \dot{J}_0 \sim \bigg[ \frac{A^2 \rho r^5 \omega_c^4}{\lambda^{3/2} N \dot{E}_0} \bigg]^{a/(a+3)} \dot{J}_0 \, .  \eeq  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{omstar2} \ref{eqn:omstar2}  and \ref{spectrum}. \ref{eqn:spectrum}.  We then substitute the value of $\dot{E}_*$ for $\dot{E}_0$ in equation \ref{omstarnl}. \ref{eqn:omstarnl}.  The appropriate value of $\omega_*$ is then $\omega_* = {\rm max} \big[ {\rm Eqn. \ref{omstar2}}, \ref{eqn:omstar2}},  {\rm Eqn.\ref{omstarnl} Eqn.\ref{eqn:omstarnl}  }\big]$. The corresponding AM flux is $\dot{J}_* \sim \Big[ \frac{\omega_*(r)}{\omega_c} \Big]^{-a} \dot{J}_0$. The cores of massive stars nearing death cool primarily through neutrino emission, so it is not unreasonable to think that waves may be damped via neutrino emission. We calculate neutrino energy loss rates in the same manner as \cite{murphy:04}. We find that neutrino damping time scales are always longer than the wave crossing timescale  \beq