Changes between Version 17 and Version 18 of doc/app/bcmequ

Timestamp:

May 12, 2020 3:36:07 PM (5 years ago)

Author:

schwenkel

Comment:

--

doc/app/bcmequ

@@ -123 +123 @@
 Note, that at the mixed phase bulk microphysics is still under development but can already applied. However, instead of prescribing it as an own scheme (as the others) it must be turned on as with  ... and is implemented as an extension of the schemes of [#seifert2006 Seifert and Beheng (2006)] and [#morrison2007 Morrison et al. (2007)].
 At this state only processes for ice crystal are included involving two further prognostic quantities: ice crystal number ''N'',,i,, and ice crystal mixing ratio ''q'',,i,,.
+
+Thus additional prognostic equations for ''N'',,i,, and ''q'',,i,, are solved:
+{{{
+#!Latex
+\begin{align*}
+ \frac{\partial N_\mathrm{i}}{\partial t} = - u_j \frac{\partial N_\mathrm{i}}{\partial x_j} - \frac{\partial}{\partial x_j}\left(\overline{u_j^{\prime\prime}N_\mathrm{i}^{\prime\prime}}\right) +   \Psi_{N_\mathrm{i}},\\
+ \frac{\partial q_\mathrm{i}}{\partial t} = - u_j
+ \frac{\partial q_\mathrm{i}}{\partial x_j} - \frac{\partial}{\partial
+   x_j}\left(\overline{u_j^{\prime\prime}q_\mathrm{i}^{\prime\prime}}\right)
+ + \Psi_{q_\mathrm{i}},
+\end{align*}
+}}}
+with the sink/source terms ''Ψ'',,Ni,, and ''Ψ'',,qi,,, and the SGS fluxes
+{{{
+#!Latex
+\begin{align*}
+  &  \overline{u_j^{\prime\prime}N_\mathrm{i}^{\prime\prime}} = -K_\mathrm{h} \:\frac{\partial N_\mathrm{i}} {\partial x_{i}}\,\\
+  & \overline{u_j^{\prime\prime}q_\mathrm{i}^{\prime\prime}} =
+  -K_\mathrm{h} \:\frac{\partial q_\mathrm{i}} {\partial
+    x_{i}}\,
+\end{align*}
+}}}
 }}}
 {{{#!td style="text-align:left;style=width: 50px"