SOME OCEAN MODEL FUNDAMENTALS
Grid cell k=kbot
Figure 8. Schematic of an ocean grid cell next to the ocean bottom labeled by k =
kbot. Its top face is a surface of constant generalized vertical coordinate s = skbotPl,
and the bottom face is determined by the ocean bottom topography at z = -H where
sbot(x, y,t) = s ( ~ ,
Y , z = -H, t).
area element along the bottom is
Hence, the transport across the solid earth boundary is
We assume that there is zero mass flux across the bottom, in which
case the advective flux drops out since v . (VH + 2) = 0 (equation
(9)). However, the possibility of a nonzero geothermal tracer transport
warrants a nonzero SGS tracer flux at the bottom, in which case the
bottom tracer flux is written
Q") = ( V H + i) J
(hot)
The corresponding thickness weighted budget is given by
and the corresponding mass budget is
I at (dr p) = d r p dM) - V, (dz p u) - (p wS))s=skbot-, .I (79)
Grid cell k=kbot
Figure 8. Schematic of an ocean grid cell next to the ocean bottom labeled by k =
kbot. Its top face is a surface of constant generalized vertical coordinate s = skbotPl,
and the bottom face is determined by the ocean bottom topography at z = -H where
sbot(x, y,t) = s ( ~ ,
Y , z = -H, t).
area element along the bottom is
Hence, the transport across the solid earth boundary is
We assume that there is zero mass flux across the bottom, in which
case the advective flux drops out since v . (VH + 2) = 0 (equation
(9)). However, the possibility of a nonzero geothermal tracer transport
warrants a nonzero SGS tracer flux at the bottom, in which case the
bottom tracer flux is written
Q") = ( V H + i) J
(hot)
The corresponding thickness weighted budget is given by
and the corresponding mass budget is
I at (dr p) = d r p dM) - V, (dz p u) - (p wS))s=skbot-, .I (79)