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Matteo Cantiello edited Convective Velocities.tex
over 9 years ago
Commit id: 619b7d7e847caa522e90bba673560269bc48274d
deletions | additions
diff --git a/Convective Velocities.tex b/Convective Velocities.tex
index f2e221f..7e2082e 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 \ln \rho}{\partial \ln \mu}
\bigg)_{\P,T} \bigg)_{\P,T}, \; \delta \equiv - \bigg(\frac{\partial \ln \rho}{\partial \ln T}
\bigg)_{\P,\mu} \bigg)_{\P,\mu}, \; \alpha \equiv \bigg(\frac{\partial \ln \rho}{\partial \ln \P} \bigg)_{\mu,T}$
and for an ideal gas $\alpha = \delta = \phi = 1$
write, assuming again pressure equilibr