deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index 27184eb..deb10e0 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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The characteristic AM flux of equation \ref{eqn:Jwaves} is positive by definition, although we expect turbulent convection to generate prograde and retrograde waves in nearly equal quantities, so that the net AM flux is nearly zero. However, differential rotation can set up powerful wave filtration mechanisms (see F14), which filter out either prograde or retrograde waves. Consider a wave packet of angular frequency $\omega$ and azimuthal number $m$ that propagates across a radial region of thickness $\Delta r$, whose endpoints have angular spin frequencies that differ by an amount $\Delta \Omega$. If $\Delta \Omega > \omega/m$, the waves will encounter a critical layer within the region, and will be absorbed. Only waves of opposing AM will penetrate through the layer, therefore, rapidly rotating regions will only permit influxes of negative AM, which will act to slow the rotation of the underlying layers.  IGW can therefore limit differential rotation to maximum of amplitudes $\Delta \Omega_{\rm max} \sim \omega/m$, provided the IGW AM flux is large enough to change the spin rate on time scales shorter than relevant stellar evolution times. In the case of a rapidly rotating core (which has contracted and spun-up) surrounded by a slowly rotating burning shell, we may expect a maximum core rotation rate of $\omega$, provided waves of this frequency can propagate into the core. This maximum rotation rate assumes $|m|=1$ waves dominate the AM flux, the actual rotation rate could be smaller if $|m|>1$ waves have a substantial impact.  Then we define a maximum core rotation rate \begin{equation}  \label{eqn:Omegamax}  \Omega_{\rm max} \sim \omega_* \,,