Changeset 991 for palm/trunk/TUTORIAL/SOURCE/sgs_models.tex

Timestamp:

Sep 5, 2012 1:09:35 PM (12 years ago)

Author:

heinze

Message:

small modifications to sgs_models.tex

File:

• palm/trunk/TUTORIAL/SOURCE/sgs_models.tex (modified) (1 diff)

palm/trunk/TUTORIAL/SOURCE/sgs_models.tex

@@ -222 +222 @@
    \end{itemize}
    $ \frac{\partial \bar{e}}{\partial t} = -\bar{u_k} \frac{\partial \bar{e}}{\partial x_k} - \tau_{ki} \frac{\partial \bar{u_i}}{\partial x_k} + \frac{g}{\Theta_0} \overline{u_3'             \Theta'} - \frac{\partial}{\partial x_k} \left\{ \overline{u_k' \left( e' + \frac{\pi'}{\rho_0} \right)} \right\} - \epsilon $                                         
-   \par\bigskip                                        
+   \par\bigskip     
+   $ \tau_{ki} = -K_{m} \left(\frac{\partial \bar{u_{i}}}{\partial x_{k}} + \frac{\partial \bar{u_{k}}}{\partial x_{i}}\right) + \frac{2}{3}\delta_{ik}\bar{e} \qquad \textnormal{with} \qquad K_{m}=0.1\cdot \Lambda \sqrt{\bar{e}}$
+   \par\bigskip   
+   $ H_{k}=\overline{u_k'\Theta'} = -K_{h}\frac{\partial\bar{\Theta}}{\partial x_{k}} \qquad  \textnormal{with} \qquad K_{h}= \left(1+2\frac{\Lambda}{\Delta}\right)$
+   \par\bigskip    
+   $W_{k}=\overline{u_k'q'} = -K_{h}\frac{\partial\bar{q}}{\partial x_{k}}$     
+            \par\bigskip 
    $ \frac{\partial}{\partial x_k} \left[ \overline{u_k' \left( e' + \frac{\pi'}{\rho_0} \right)} \right] = - \frac{\partial}{\partial x_k} \nu_e \frac{\partial \bar{e}}{\partial x_k} $
    \par\bigskip