this is for holding javascript data
Matteo Cantiello edited Convective Velocities.tex
over 9 years ago
Commit id: 5218df3fdacfa510a9a3ee050c6b613782f71983
deletions | additions
diff --git a/Convective Velocities.tex b/Convective Velocities.tex
index 7e2082e..cbf5df2 100644
--- a/Convective Velocities.tex
+++ b/Convective Velocities.tex
...
\frac{\D\rho}{\rho} = \alpha \frac{\D\P}{\P} - \delta \frac{\D T}{T} + \phi {\D\mu}{\mu}
\end{equation}
Where
$ \phi \equiv
\bigg(\frac{\partial \big(\frac{\partial \ln \rho}{\partial \ln \mu}
\bigg)_{\P,T}, \big)_{\P,T}, \; \delta \equiv -
\bigg(\frac{\partial \big(\frac{\partial \ln \rho}{\partial \ln T}
\bigg)_{\P,\mu}, \big)_{\P,\mu}, \; \alpha \equiv
\bigg(\frac{\partial \big(\frac{\partial \ln \rho}{\partial \ln \P}
\bigg)_{\mu,T}$ \big)_{\mu,T}$
and for an ideal gas $\alpha = \delta = \phi = 1$
write, assuming again pressure equilibr