Changeset 991


Ignore:
Timestamp:
Sep 5, 2012 1:09:35 PM (9 years ago)
Author:
heinze
Message:

small modifications to sgs_models.tex

File:
1 edited

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  • palm/trunk/TUTORIAL/SOURCE/sgs_models.tex

    r987 r991  
    222222   \end{itemize}
    223223   $ \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 $                                         
    224    \par\bigskip                                       
     224   \par\bigskip     
     225   $ \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}}$
     226   \par\bigskip   
     227   $ 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)$
     228   \par\bigskip   
     229   $W_{k}=\overline{u_k'q'} = -K_{h}\frac{\partial\bar{q}}{\partial x_{k}}$     
     230            \par\bigskip
    225231   $ \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} $
    226232   \par\bigskip
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