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2.14.1 Advection of momentum

The advective operator is second order accurate in space:

$\displaystyle {\cal A}_w \Delta r_f h_w G_u^{adv}$ $\displaystyle =$ $\displaystyle \delta_i \overline{ U }^i \overline{ u }^i + \delta_j \overline{ V }^i \overline{ u }^j + \delta_k \overline{ W }^i \overline{ u }^k$ (2.97)
$\displaystyle {\cal A}_s \Delta r_f h_s G_v^{adv}$ $\displaystyle =$ $\displaystyle \delta_i \overline{ U }^j \overline{ v }^i + \delta_j \overline{ V }^j \overline{ v }^j + \delta_k \overline{ W }^j \overline{ v }^k$ (2.98)
$\displaystyle {\cal A}_c \Delta r_c G_w^{adv}$ $\displaystyle =$ $\displaystyle \delta_i \overline{ U }^k \overline{ w }^i + \delta_j \overline{ V }^k \overline{ w }^j + \delta_k \overline{ W }^k \overline{ w }^k$ (2.99)

and because of the flux form does not contribute to the global budget of linear momentum. The quantities $ U$ , $ V$ and $ W$ are volume fluxes defined:
$\displaystyle U$ $\displaystyle =$ $\displaystyle \Delta y_g \Delta r_f h_w u$ (2.100)
$\displaystyle V$ $\displaystyle =$ $\displaystyle \Delta x_g \Delta r_f h_s v$ (2.101)
$\displaystyle W$ $\displaystyle =$ $\displaystyle {\cal A}_c w$ (2.102)

The advection of momentum takes the same form as the advection of tracers but by a translated advective flow. Consequently, the conservation of second moments, derived for tracers later, applies to $ u^2$ and $ v^2$ and $ w^2$ so that advection of momentum correctly conserves kinetic energy.

\fbox{ \begin{minipage}{4.75in} {\em S/R MOM\_U\_ADV\_UU} ({\em mom\_u\_adv\_uu.... ...u$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em mom\_fluxform.F}) \end{minipage} }

next up previous contents
Next: 2.14.2 Coriolis terms Up: 2.14 Flux-form momentum equations Previous: 2.14 Flux-form momentum equations   Contents
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