Matteo Cantiello edited Convective Velocities.tex  over 9 years ago

Commit id: 5218df3fdacfa510a9a3ee050c6b613782f71983

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\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