Merge remote-tracking branch 'upstream/development' into development

Docs/sphinx_doc/theory/Buoyancy.rst

@@ -7,6 +7,29 @@
 
 .. _Buoyancy:
 
+Density of the mixture
+========================
+
+The total density in a given cell is given by
+
+.. math::
+    \rho = \frac{m}{V} = \frac{m_a + m_v + m_c + m_p}{V},
+
+where :math:`m_a` is the mass of dry air, :math:`m_v` is the mass of water vapor, :math:`m_c` is the mass of liquid water, and :math:`m_p` is the mass of precipitate.
+From the definitions of the mass mixing ratio (ratio of mass of a component to mass of dry air), we have for any component
+
+.. math::
+    q_i \equiv = \frac{m_i}{m_a}.
+
+Using this we can write
+
+.. math::
+    \rho = m_a\frac{(1 + q_v + q_c + q_p)}{V}
+          = \rho_d(1 + q_v + q_c + q_p),
+
+where :math:`\rho_d \equiv \cfrac{m_a}{V}` is the density of dry air.
+
+
 Buoyancy
 =========