Changeset 988 for palm/trunk/DOC/tec/methods
 Timestamp:
 Sep 5, 2012 11:27:58 AM (9 years ago)
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 palm/trunk/DOC/tec/methods/cloud_physics
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palm/trunk/DOC/tec/methods/cloud_physics/cloud_physics.tex
r701 r988 43 43 \linebreak 44 44 14.12.2009 45 \linebreak 46 \linebreak 47 last update 48 \linebreak 49 \today 45 50 \end{center} 46 51 … … 62 67 \end{itemize} 63 68 The dynamical processes are covered by advection and diffusion and they are described by the implemented methods. For the consideration of the 64 thermodynamical processes modifications are necessary in the thermodynamics of PALM 69 thermodynamical processes modifications are necessary in the thermodynamics of PALM. In doing so evaporation and condensation are treated as 65 70 adiabatic processes whereas precipitation and radiation are treated as diabatic processes. In the dry version of PALM the thermodynamic variable 66 71 is the potential temperature $\theta$. The first law of thermodynamics provides the prognostic equation … … 137 142 \frac{\partial \left(\overline u_{j} \overline q\right)}{\partial x_{j}} 138 143 \frac{\partial\, \overline{u_{j}^{'} q^{'}}}{\partial x_{j}} 139 +\left(\frac{\partial \overline q}{\partial t}\right)_{\mathrm{ RAD}}144 +\left(\frac{\partial \overline q}{\partial t}\right)_{\mathrm{PREC}} 140 145 \label{eq:total_water} 141 146 \end{eqnarray} … … 348 353 \left(\frac{\partial \overline q}{\partial t}\right)_{\mathrm{PREC}} & = & 349 354 \begin{cases} 350 \left(\overline q_{l}\overline q_{l_{\mathrm{crit}}}\right) \cdot\tau &355 \left(\overline q_{l}\overline q_{l_{\mathrm{crit}}}\right)/ \tau & 351 356 \quad\overline q_{l} > \overline q_{l_{\mathrm{crit}}} \\ 352 357 0 & \quad\overline q_{l} \leq \overline q_{l_{\mathrm{crit}}} … … 356 361 The precipitation leaves the grid volume immediately if the threshold of the liquid water content 357 362 $\overline q_{l_{\mathrm{crit}}}=0.5\,\mathrm{g/kg}$ is exceeded. Hence, evaporation of the rain drops does not occur. 358 $\tau$ is a time scale with a value of 0.001\,s.363 $\tau$ is a time scale with a value of 1000\,s. 359 364 \newline 360 365 The influence of the precipitation on the temperature is as follows:
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