54
STEPHEN GRIFFIES
horizontal convergence of pressure and viscous stresses. The sixth and
seventh terms arise from the frictional and pressure stresses acting on
the constant generalized surfaces. These forces provide an interfacial
stress between layers of constant s. Note that even in the absence of
frictional stresses, interfacial stresses from pressure acting on the generally curved s surface can transmit momentum between vertically stacked
layers. The final term arises from the gravitational force, the Coriolis
force, and the advective frequency.
4.3
Cell adjacent to the ocean bottom
As for the tracer and mass budgets, we assume zero mass flux through
the ocean bottom at z = - H (x, y). However, there is generally a nonzero
stress at the bottom due to both the pressure between the fluid and the
bottom, and unresolved features in the flow which can correlate or anticorrelate with bottom topographic features (Holloway, 1999). The area
integral of the stresses lead to a force on the fluid at the bottom
Details of the stress term requires fine scale information that is generally
unavailable. For present purposes we assume that some boundary layer
model provides information that is schematically written
where T~~~ is a vector bottom stress. Taking the limit as the horizontal
area vanishes leads to the thickness weighted budget for momentum per
horizontal area of a grid cell next to the ocean bottom
There is a nonzero mass and momentum flux through the upper ocean
surface at z = q(x, y, t ) , and contact stresses are applied from resolved
and unresolved processes involving interactions with the atmosphere and
STEPHEN GRIFFIES
horizontal convergence of pressure and viscous stresses. The sixth and
seventh terms arise from the frictional and pressure stresses acting on
the constant generalized surfaces. These forces provide an interfacial
stress between layers of constant s. Note that even in the absence of
frictional stresses, interfacial stresses from pressure acting on the generally curved s surface can transmit momentum between vertically stacked
layers. The final term arises from the gravitational force, the Coriolis
force, and the advective frequency.
4.3
Cell adjacent to the ocean bottom
As for the tracer and mass budgets, we assume zero mass flux through
the ocean bottom at z = - H (x, y). However, there is generally a nonzero
stress at the bottom due to both the pressure between the fluid and the
bottom, and unresolved features in the flow which can correlate or anticorrelate with bottom topographic features (Holloway, 1999). The area
integral of the stresses lead to a force on the fluid at the bottom
Details of the stress term requires fine scale information that is generally
unavailable. For present purposes we assume that some boundary layer
model provides information that is schematically written
where T~~~ is a vector bottom stress. Taking the limit as the horizontal
area vanishes leads to the thickness weighted budget for momentum per
horizontal area of a grid cell next to the ocean bottom
There is a nonzero mass and momentum flux through the upper ocean
surface at z = q(x, y, t ) , and contact stresses are applied from resolved
and unresolved processes involving interactions with the atmosphere and