OCEAN MODELS
95
Regarding low frequency motions, the statistical effect of unresolved
topographic roughness has been explored in the framework of the quasigeostrophic (QG) equations, starting with Rhines (1977). The main
effect of bottom roughness is to scatter the barotropic energy into baroclinic modes, and decrease the energy of mesoscale motions in the deep
layers. There has been no attempt to parameterize this effect in ocean
models. On the contrary, the effect of bottom roughness is probably
overestimated already in standard z-coordinate models with unsmoothed
staircase topography. Penduff et al. (2002) show that in such a model
the eddy kinetic energy below 1000 m is lower than in a σ-coordinate
model, the latter being in better agreement with observations. By performing sensitivity experiments with the z model they show that the
grid-scale topographic roughness is responsible for a too rapid decay of
the eddy kinetic energy with depth.
Beside allowing overflows, deep passages and fracture zones often act
to sharpen and focus fronts. This effect can influence the whole water
column when major currents cross topographic ridges. One example is
the flow of the North Atlantic current across the Mid Atlantic ridge,
which seems to be distributed in three branches corresponding to three
fracture zones (Bower et al., 2002). There is no parameterization of this
effect in low resolution models.
4.
Lateral mixing parameterizations
4.1
Prandtl number
Let us assume that lateral momentum and tracer mixing are parameterized as laplacian operators with turbulent viscosity ν and diffusivity
κ. The ratio of viscosity to diffusivity is the Prandtl number, P r = ν/κ.
For molecular viscosity and heat diffusivity in sea water, it varies from
13 (at 0 ◦ C) to 7 (at 20 ◦ C). Molecular values are irrelevant at the scale
of ocean models, and the Prandlt numbers used in models parameterizations vary widely. This is not based on physics but rather the result of
numerical stability constraints which seem more stringent on viscosity
than diffusivity. In low resolution climate models, Prandtl numbers as
high as 50 can be found.
At the scale of quasi-geostrophic eddies, the Prandtl number could
be one if one accepts that QG eddies essentially mix potential vorticity.
In that case, mixing of vortex stretching (with diffusivity κ) has to be
the same as mixing of relative vorticity (with viscosity ν). At the submesoscale, I do not know of theories nor observations that would guide
modellers in a choice of Prandtl number.
95
Regarding low frequency motions, the statistical effect of unresolved
topographic roughness has been explored in the framework of the quasigeostrophic (QG) equations, starting with Rhines (1977). The main
effect of bottom roughness is to scatter the barotropic energy into baroclinic modes, and decrease the energy of mesoscale motions in the deep
layers. There has been no attempt to parameterize this effect in ocean
models. On the contrary, the effect of bottom roughness is probably
overestimated already in standard z-coordinate models with unsmoothed
staircase topography. Penduff et al. (2002) show that in such a model
the eddy kinetic energy below 1000 m is lower than in a σ-coordinate
model, the latter being in better agreement with observations. By performing sensitivity experiments with the z model they show that the
grid-scale topographic roughness is responsible for a too rapid decay of
the eddy kinetic energy with depth.
Beside allowing overflows, deep passages and fracture zones often act
to sharpen and focus fronts. This effect can influence the whole water
column when major currents cross topographic ridges. One example is
the flow of the North Atlantic current across the Mid Atlantic ridge,
which seems to be distributed in three branches corresponding to three
fracture zones (Bower et al., 2002). There is no parameterization of this
effect in low resolution models.
4.
Lateral mixing parameterizations
4.1
Prandtl number
Let us assume that lateral momentum and tracer mixing are parameterized as laplacian operators with turbulent viscosity ν and diffusivity
κ. The ratio of viscosity to diffusivity is the Prandtl number, P r = ν/κ.
For molecular viscosity and heat diffusivity in sea water, it varies from
13 (at 0 ◦ C) to 7 (at 20 ◦ C). Molecular values are irrelevant at the scale
of ocean models, and the Prandlt numbers used in models parameterizations vary widely. This is not based on physics but rather the result of
numerical stability constraints which seem more stringent on viscosity
than diffusivity. In low resolution climate models, Prandtl numbers as
high as 50 can be found.
At the scale of quasi-geostrophic eddies, the Prandtl number could
be one if one accepts that QG eddies essentially mix potential vorticity.
In that case, mixing of vortex stretching (with diffusivity κ) has to be
the same as mixing of relative vorticity (with viscosity ν). At the submesoscale, I do not know of theories nor observations that would guide
modellers in a choice of Prandtl number.