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Next: 2.14.3 Curvature metric terms Up: 2.14 Flux-form momentum equations Previous: 2.14.1 Advection of momentum   Contents

2.14.2 Coriolis terms

The ``pure C grid'' Coriolis terms (i.e. in absence of C-D scheme) are discretized:

$\displaystyle {\cal A}_w \Delta r_f h_w G_u^{Cor}$ $\displaystyle =$ $\displaystyle \overline{ f {\cal A}_c \Delta r_f h_c \overline{ v }^j }^i - \epsilon_{nh} \overline{ f' {\cal A}_c \Delta r_f h_c \overline{ w }^k }^i$ (2.103)
$\displaystyle {\cal A}_s \Delta r_f h_s G_v^{Cor}$ $\displaystyle =$ $\displaystyle - \overline{ f {\cal A}_c \Delta r_f h_c \overline{ u }^i }^j$ (2.104)
$\displaystyle {\cal A}_c \Delta r_c G_w^{Cor}$ $\displaystyle =$ $\displaystyle \epsilon_{nh} \overline{ f' {\cal A}_c \Delta r_f h_c \overline{ u }^i }^k$ (2.105)

where the Coriolis parameters $ f$ and $ f'$ are defined:
$\displaystyle f$ $\displaystyle =$ $\displaystyle 2 \Omega \sin{\varphi}$ (2.106)
$\displaystyle f'$ $\displaystyle =$ $\displaystyle 2 \Omega \cos{\varphi}$ (2.107)

where $ \varphi $ is geographic latitude when using spherical geometry, otherwise the $ \beta$ -plane definition is used:
$\displaystyle f$ $\displaystyle =$ $\displaystyle f_o + \beta y$ (2.108)
$\displaystyle f'$ $\displaystyle =$ 0 (2.109)

This discretization globally conserves kinetic energy. It should be noted that despite the use of this discretization in former publications, all calculations to date have used the following different discretization:

$\displaystyle G_u^{Cor}$ $\displaystyle =$ $\displaystyle f_u \overline{ v }^{ji} - \epsilon_{nh} f_u' \overline{ w }^{ik}$ (2.110)
$\displaystyle G_v^{Cor}$ $\displaystyle =$ $\displaystyle - f_v \overline{ u }^{ij}$ (2.111)
$\displaystyle G_w^{Cor}$ $\displaystyle =$ $\displaystyle \epsilon_{nh} f_w' \overline{ u }^{ik}$ (2.112)

where the subscripts on $ f$ and $ f'$ indicate evaluation of the Coriolis parameters at the appropriate points in space. The above discretization does not conserve anything, especially energy and for historical reasons is the default for the code. A flag controls this discretization: set run-time logical useEnergyConservingCoriolis to true which otherwise defaults to false.

\fbox{ \begin{minipage}{4.75in} {\em S/R MOM\_CDSCHEME} ({\em mom\_cdscheme.F}) ... ...^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em mom\_fluxform.F}) \end{minipage} }

next up previous contents
Next: 2.14.3 Curvature metric terms Up: 2.14 Flux-form momentum equations Previous: 2.14.1 Advection of momentum   Contents
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