Changes between Version 5 and Version 6 of doc/tec/gov

Timestamp:

Apr 7, 2016 3:58:42 PM (9 years ago)

Author:

Giersch

Comment:

--

doc/tec/gov

@@ -3 +3 @@
 = Governing equations =
 By default, PALM has six prognostic quantities: the velocity components ''u'', ''v'', ''w'' on a Cartesian grid, the potential temperature ''θ'', specific humidity ''q'',,v,, or a passive scalar ''s'', and the SGS turbulent kinetic energy (SGS-TKE) ''e''. The separation of resolved scales and SGS is implicitly achieved by averaging the governing equations over discrete Cartesian grid volumes as proposed by [#schumann1975 Schumann (1975)]. Moreover, it is possible to run PALM in a direct numerical simulation mode by switching off the prognostic equation for the SGS-TKE and setting a constant eddy diffusivity. For a list of all symbols and parameters, that we will introduce in this section, see the following Table 1 and 2.
- 
 
-[[Image(Table1.png,600px)]]
-[[Image(Table2.png,600px)]]
+
+[[Image(Table1.png,600px,border=1)]]
+[[Image(Table2.png,600px),border=1)]]
 
 
@@ -21 +21 @@
 }}}
 Here, ''i'', ''j'', ''k'' ∈ {1, 2, 3}. ''u'',,i,, are the velocity components (''u,,1,, = u, u,,2,, = v, u,,3,, = w'') with location ''x'',,i,, (''x,,1,, = x, x,,2,, = y, x,,3,, = z''), ''t'' is time, ''f,,i,, = (0, 2 Ω cos(φ), 2 Ω
-sin(φ))'' is the Coriolis parameter with ''Ω'' being the Earth's angular velocity and ''φ'' being the geographical latitude. ''u'',,g,k,, are the geostrophic wind speed components, ''ρ'',,0,, is the density of dry air, ''π^∗^ = p^∗^ + 2/3 ρ,,0,, e '' is the modified perturbation pressure with ''p^∗^'' being the perturbation pressure and the SGS-TKE ''e = 1/2 u^″^,,i,,u^″^,,i,,'' 
+sin(φ))'' is the Coriolis parameter with ''Ω'' being the Earth's angular velocity and ''φ'' being the geographical latitude. ''u'',,g,k,, are the geostrophic wind speed components, ''ρ'',,0,, is the density of dry air, ''π^∗^ = p^∗^ + 2/3 ρ,,0,, e '' is the modified perturbation pressure with ''p^∗^'' being the perturbation pressure and the SGS-TKE 
+{{{
+#!Latex
+$e =
+\frac{1}{2} \overline{u_i^{\prime\prime} u_i^{\prime\prime}}$
+}}}
+
 == References ==
 * [=#schumann1975]'''Schumann U.''' 1975. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18: 376–404.