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Next: 2.14.4 Shear terms Up: 2.14 Vector invariant momentum Previous: 2.14.2 Kinetic energy   Contents

2.14.3 Coriolis terms

The potential enstrophy conserving form of the linear Coriolis terms are written:

$\displaystyle G_u^{fv}$ $\displaystyle =$ $\displaystyle \frac{1}{\Delta x_c} \overline{ \frac{f}{h_\zeta} }^j \overline{ \overline{ \Delta x_g h_s v }^j }^i$ (2.147)
$\displaystyle G_v^{fu}$ $\displaystyle =$ $\displaystyle - \frac{1}{\Delta y_c} \overline{ \frac{f}{h_\zeta} }^i \overline{ \overline{ \Delta y_g h_w u }^i }^j$ (2.148)

Here, the Coriolis parameter $ f$ is defined at vorticity (corner) points.

The potential enstrophy conserving form of the non-linear Coriolis terms are written:

$\displaystyle G_u^{\zeta_3 v}$ $\displaystyle =$ $\displaystyle \frac{1}{\Delta x_c} \overline{ \frac{\zeta_3}{h_\zeta} }^j \overline{ \overline{ \Delta x_g h_s v }^j }^i$ (2.149)
$\displaystyle G_v^{\zeta_3 u}$ $\displaystyle =$ $\displaystyle - \frac{1}{\Delta y_c} \overline{ \frac{\zeta_3}{h_\zeta} }^i \overline{ \overline{ \Delta y_g h_w u }^i }^j$ (2.150)

The Coriolis terms can also be evaluated together and expressed in terms of absolute vorticity $ f+\zeta_3$. The potential enstrophy conserving form using the absolute vorticity is written:

$\displaystyle G_u^{fv} + G_u^{\zeta_3 v}$ $\displaystyle =$ $\displaystyle \frac{1}{\Delta x_c} \overline{ \frac{f + \zeta_3}{h_\zeta} }^j \overline{ \overline{ \Delta x_g h_s v }^j }^i$ (2.151)
$\displaystyle G_v^{fu} + G_v^{\zeta_3 u}$ $\displaystyle =$ $\displaystyle - \frac{1}{\Delta y_c} \overline{ \frac{f + \zeta_3}{h_\zeta} }^i \overline{ \overline{ \Delta y_g h_w u }^i }^j$ (2.152)

The distinction between using absolute vorticity or relative vorticity is useful when constructing higher order advection schemes; monotone advection of relative vorticity behaves differently to monotone advection of absolute vorticity. Currently the choice of relative/absolute vorticity, centered/upwind/high order advection is available only through commented subroutine calls.

\fbox{ \begin{minipage}{4.75in} {\em S/R MOM\_VI\_CORIOLIS} ({\em mom\_vi\_corio... ... $G_v^{\zeta_3 u}$: {\bf vCf} (local to {\em calc\_mom\_rhs.F}) \end{minipage} }

next up previous contents
Next: 2.14.4 Shear terms Up: 2.14 Vector invariant momentum Previous: 2.14.2 Kinetic energy   Contents
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