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Next: 2.15.8 Vertical dissipation Up: 2.15 Vector invariant momentum Previous: 2.15.6 Horizontal divergence   Contents

2.15.7 Horizontal dissipation

The following discretization of horizontal dissipation conserves potential vorticity (thickness weighted relative vorticity) and divergence and dissipates energy, enstrophy and divergence squared:

$\displaystyle G_u^{h-dissip}$ $\displaystyle =$ $\displaystyle \frac{1}{\Delta x_c} \delta_i ( A_D D - A_{D4} D^*) - \frac{1}{\Delta y_u h_w} \delta_j h_\zeta ( A_\zeta \zeta - A_{\zeta4} \zeta^* )$ (2.158)
$\displaystyle G_v^{h-dissip}$ $\displaystyle =$ $\displaystyle \frac{1}{\Delta x_v h_s} \delta_i h_\zeta ( A_\zeta \zeta - A_\zeta \zeta^* ) + \frac{1}{\Delta y_c} \delta_j ( A_D D - A_{D4} D^* )$ (2.159)

where
$\displaystyle D^*$ $\displaystyle =$ $\displaystyle \frac{1}{{\cal A}_c h_c} ( \delta_i \Delta y_g h_w \nabla^2 u + \delta_j \Delta x_g h_s \nabla^2 v )$ (2.160)
$\displaystyle \zeta^*$ $\displaystyle =$ $\displaystyle \frac{1}{{\cal A}_\zeta} ( \delta_i \Delta y_c \nabla^2 v - \delta_j \Delta x_c \nabla^2 u )$ (2.161)

\fbox{ \begin{minipage}{4.75in} {\em S/R MOM\_VI\_HDISSIP} ({\em mom\_vi\_hdissi... ...ar $G_v^{h-dissip}$: {\bf vDiss} (local to {\em mom\_vecinv.F}) \end{minipage} }


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