Changes between Version 6 and Version 7 of doc/tec/gov

Timestamp:

Apr 13, 2016 3:57:17 PM (9 years ago)

Author:

Giersch

Comment:

--

doc/tec/gov

@@ -13 +13 @@
 #!Latex
 \begin{align*}
- \frac{\partial u_i}{\partial t}&= - \frac{\partial u_i u_j}{\partial x_j} -\varepsilon_{ijk}f_j u_k + \varepsilon_{i3j}f_3 {u_{\mathrm{g},j}} - \frac{1}{\rho_0} \frac{\partial \pi^\ast}{\partial x_i} + g \frac{\theta_\mathrm{v} - \langle\theta_{\mathrm{v}}\rangle}{\langle\theta_{\mathrm{v}}\rangle}\delta_{i3}-\frac{\partial}{\partial x_j} \left(\overline{u_i^{\prime\prime} u_j^{\prime\prime}} - \frac{2}{3}e\delta_{ij}\right), \\
+ \frac{\partial u_i}{\partial t} &= - \frac{\partial u_i u_j}{\partial x_j} -\varepsilon_{ijk}f_j u_k + \varepsilon_{i3j}f_3 {u_{\mathrm{g},j}} - \frac{1}{\rho_0} \frac{\partial \pi^\ast}{\partial x_i} + g \frac{\theta_\mathrm{v} - \langle\theta_{\mathrm{v}}\rangle}{\langle\theta_{\mathrm{v}}\rangle}\delta_{i3}-\frac{\partial}{\partial x_j} \left(\overline{u_i^{\prime\prime} u_j^{\prime\prime}} - \frac{2}{3}e\delta_{ij}\right), \\
  \frac{\partial u_j}{\partial x_j}&=0, \\
  \frac{\partial \theta}{\partial t} &= - \frac{\partial u_j \theta}{\partial x_j} -\frac{\partial}{\partial x_j}\left(\overline{u_j^{\prime\prime}\theta^{\prime\prime}}\right) - \frac{L_\mathrm{V}}{c_p \Pi} \Psi_{q_\mathrm{v}}, \\
@@ -24 +24 @@
 {{{
 #!Latex
-$e =
-\frac{1}{2} \overline{u_i^{\prime\prime} u_i^{\prime\prime}}$
+\begin{align*}
+e = \frac{1}{2} \overline{u_i^{\prime\prime} u_i^{\prime\prime}},
+\end{align*}
 }}}
+and ''g'' is the gravitational acceleration. The potential temperature is defined as
+{{{
+#!Latex
+\begin{align*}
+ \theta = T/\,\Pi,
+\end{align*}
+}}}
+with the current absolute temperature ''T'' and the Exner function
+{{{
+#!Latex
+\begin{align*}
+  & \Pi = \left(\frac{p}{p_0}\right)^{R_\mathrm{d}/c_p},
+\end{align*}
+}}}
+with ''p'' being the hydrostatic air pressure, ''p'',,0,, = 1000 hPa a reference pressure, ''R'',,d,, the specific gas constant for dry
+air, and ''c'',,p,, the specific heat of dry air at constant pressure. The virtual potential temperature is defined as
+{{{
+#!Latex
+\begin{align*}
+  & \theta_\mathrm{v} = \theta \left[1+\left(\frac{R_\mathrm{v}}{R_\mathrm{d}}-1\right) q_\mathrm{v} - q_\mathrm{l}\right],
+\end{align*}
+}}}
+with the specific gas constant for water vapor ''R'',,v,,, and the liquid water specific humidity ''q'',,l,,. For the computation of ''q'',,l,,, see the descriptions of the embedded cloud microphysical models in Sects. ~\ref{sec:micro} and \ref{sec:lcm}. Furthermore,
+''L'',,V,, is the latent heat of vaporization, and ''Ψ'',,q,,v,,,, and ''Ψ'',,s,, are source/sink terms of ''q'',,v,, and ''s'', respectively.
 
 == References ==