Changes between Version 13 and Version 14 of doc/tec/advection

Timestamp:

Mar 23, 2011 3:00:39 PM (14 years ago)

Author:

suehring

Comment:

--

doc/tec/advection

@@ -67 +67 @@
 === Statistical evaluation of turbulent fluxes ===
 
-The statistical evaluation of turbulent fluxes should be consistent with the discretization in the prognostic equations because otherwise some unphysical effects occur. For example the computation of the turbulent fluxes as variances and covariances induces some conspicuous kinks in the vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. In order to compute the turbulent fluxes as they appear in the prognostic equations, the fluxes are computed in the advection routines, buffered and then reused for the statistics. To receive the turbulent and not the mean signal and to remove the influence of Galilei transformation, the centered flux F,,i+1/2,, has to be multiplied with a factor 
+The statistical evaluation of turbulent fluxes should be consistent with the discretization in the prognostic equations because otherwise some unphysical effects occur. For example the computation of the turbulent fluxes as variances and covariances induces some conspicuous kinks in the vertical heat and momentum fluxes near the surface, while the temperature and velocity profiles show no conspicuity. In order to compute the turbulent fluxes as they appear in the prognostic equations, the fluxes are computed in the advection routines, buffered and then reused for the statistics. To receive the turbulent and not the mean signal and to remove the influence of Galilei transformation, the centered fraction of the flux F,,i+1/2,, has to be multiplied with a factor 
 {{{
 #!Latex
-\[ \frac{u_{i+\frac{1}{2}} - 2 \overline u}{u_{i+\frac{1}{2}} - u_{i, Galilei}} \] 
+\[ \frac{u_{i+\frac{1}{2}} - \overline u}{u_{i+\frac{1}{2}} - u_{i, Galilei}} \] 
 }}}
-and the dissipative flux has to be multiplied with a factor
+and the dissipative fraction with a factor
 {{{
 #!Latex
-\[ \frac{|u_{i+\frac{1}{2}} - 2 \overline u|}{|u_{i+\frac{1}{2}} - u_{i, Galilei}|}, \] 
+\[ \frac{|u_{i+\frac{1}{2}} - \overline u|}{|u_{i+\frac{1}{2}} - u_{i, Galilei}|}, \] 
 }}}
 where u denotes the corresponding velocity component. Furthermore, the turbulent fluxes are evaluated on each Runge-Kutta substep and weighted with the respective Runge-Kutta coefficients to remove dependencies of the Runge-Kutta substeps. The interpretation of the turbulent fluxes as variances and covariances is no longer valid when using WS5. For other advection schemes, like the PW-scheme, the interpretation of turbulent fluxes as co/variances is still valid, because the discretization is alike the computation of the co/variances.