Changes between Version 51 and Version 52 of doc/tec/bc

Timestamp:

Nov 19, 2018 11:59:15 AM (6 years ago)

Author:

suehring

Comment:

--

doc/tec/bc

@@ -313 +313 @@
 #!Latex
 \begin{equation*}
-R_{i,i} = u_{*}^2\,( 0.35\,(-\frac{z_i}{\kappa\,L})^\frac{2}{3}) + (5 - 4\,\frac{z}{z_i}) )\,, \: (i \in (1,2)\,,
+R_{i,i} = u_{*}^2\,( 0.35\,(-\frac{z_i}{\kappa\,L})^\frac{2}{3} + (5 - 4\,\frac{z}{z_i}) )\,, \: (i \in (1,2)\,,
 \end{equation*}
 }}}
@@ -326 +326 @@
 #!Latex
 \begin{equation*}
-R_{i,i} = w_{m}^2\,( 1.5\,(\frac{z}{z_i})^\frac{2}{3}\,\exp{-2\,\frac{z}{z_i}} + (1.7 - \frac{z}{z_i})\,(\frac{u_{*}}{w_m})^2)\,, \: (i \in (3)\,,
+R_{i,i} = w_{m}^2\,( 1.5\,(\frac{z}{z_i})^\frac{2}{3}\,e^(-2\,\frac{z}{z_i}) + (1.7 - \frac{z}{z_i})\,(\frac{u_{*}}{w_m})^2)\,, \: (i \in (3)\,,
 \end{equation*}
 }}}
@@ -337 +337 @@
 }}}
 being the momentum velocity scale, with the convective velocity scale ''w,,*,,''. In case of stable or neutral stratification, ''w,,m,, = u,,*,,''.  
-
-
+The remaining components ''R,,31,,,R,,32,,,R,,21,,'' are parametrized as
+{{{
+#!Latex
+\begin{equation*}
+R_{i,j} = u_{*}^2\,( 1 - e^(3\,\frac{z}{z_i} - 1))\,.
+\end{equation*}
+}}}
+
+Too date, no proper parametrization of turbulent length scales that works for all stability regimes and within the entire boundary layer is available. 
+Hence, for the moment the integral length scales are set to
+ {{{
+#!Latex
+\begin{equation*}
+l_{i,j} = 8\cdot \MIN( \Delta x_i ) , \: i \in (1,2,3)\,,
+\end{equation*}
+}}}
+which arises from following considerations: On the one hand, from the numerical point of view the imposed perturbations should not be rapidly eliminated by the numerics. 
+The numerical dissipation and dispersion, however, act on scales up to 8 time the grid spacing (5th order scheme, see: wiki:/doc/tec/discret]), meaning that scales < 8 times the grid spacing are rapidly dispersed and dissipated due to numerical errors. In order to trigger further turbulence development within the model domain, the imposed correlated turbulence should be on scales larger than the numerically-affected scales. 
+On the other hand, however, imposing too large length scales could trigger structures that exist throughout the entire model domain, particularly under stable conditions, which in turn could bias the simulation results. 
+Hence, as a compromise, length scales are set to 8 time the minimum grid spacing. 
+
+
+Note, for ''z''>''z,,i,,'' the components of the stress tensor are set to zero so that effectively no synthetic turbulence is imposed above the boundary-layer height.
+ 
 method 2 undergoes testing