Changes between Version 14 and Version 15 of doc/tec/sgs

Timestamp:

Mar 27, 2020 1:17:57 PM (4 years ago)

Author:

maronga

Comment:

--

doc/tec/sgs

@@ -46 +46 @@
  \frac{\partial{\theta_{\mathrm{v}}}}{\partial z}\right)^{-\frac{1}{2}} \right) &\text{for~}
     \frac{\partial{\theta_{\mathrm{v}}}}{\partial z} > 0, \\
- \\boldsymbol{\varDelta} &\text{for~}    \frac{\partial{\theta_{\mathrm{v}}}}{\partial z} \leq 0.
+ \boldsymbol{\varDelta} &\text{for~}    \frac{\partial{\theta_{\mathrm{v}}}}{\partial z} \leq 0.
 \end{cases}
 \end{align*}
@@ -110 +110 @@
 
 == [=#deardorff_sgs-dai Modified Deardorff subgrid-scale model] ==
-A modificaiton of the Deardorff scheme described above is available that provides an improved mixing length calculation for locally stable stratification, particularly if used with fine grid spacings. Details about the deficiencies of the Deardorff scheme and the following modified version are given by [#dai Dai et al. (2020)]. In the following, we only describe the modifications of the Deardorff scheme.
-
-The mixing length is calculated as
+A modificaiton of the Deardorff scheme described above is available that provides an improved mixing length calculation for locally stable stratification, particularly if used with fine grid spacings. Details about the deficiencies of the Deardorff scheme and the following modified version are given by [#dai Dai et al. (2020)]. In the following, we only describe the two modifications that are applied to the Deardorff scheme described above.
+
+First, the mixing length is calculated as
 {{{
 #!Latex
@@ -125 +125 @@
 }}}
 
+Seocnd, the eddy diffusivities are defined as
+{{{
+#!Latex
+\begin{align*}
+   & K_h =
+ \begin{cases}
+ K_h = K_m                                     & \frac{\partial{\theta_{\mathrm{v}}}}{\partial z} > 0, \\
+ K_h = 3 K_m & \text{for~} \frac{\partial{\theta_{\mathrm{v}}}}{\partial z} \leq 0.
+\end{cases}
+\end{align*}
+
 == [=#dynamic_sgs Dynamic subgrid-scale model] ==