100
ANNE-MARIE TREGUIER
els it has mainly been used in MICOM (Bleck and Boudra, 1981). A
study by Griffies and Hallberg (2003) suggests that using a biharmonic
operator with Smagorinsky-like viscosity is better in eddy permitting
simulation when the flow is non homogeneous (in the presence of western boundary currents, for instance) because it allows lower levels of
viscosity in the interior.
This short review emphasizes numerical constraints as the basis for
the choice of parameterizations of momentum mixing. We can hope
that more physically based parameterizations will emerge in the future.
Smith and McWilliams (2003) have developed a promising framework
by deriving a general form for anisotropic viscosity, and an elegant functional form for the discretization following a similar work by Griffies
et al. (1998) on the isoneutral diffusion.
For completeness we must mention here another approach to parameterizations. It consists in using the properties of numerical advections
schemes to represent the cascade of enstrophy to small scales (this also
applies to cascade of tracer variance reviewed in the previous section).
With that strategy, no explicit parameterization is needed. Shchepetkin
and McWiliams (1998) advocate this approach, claiming that higher
Reynolds numbers can be simulated that way, compared with the combination of a classical advection scheme and hyperviscosity. Those authors also claim that it is more computationaly efficient to increase the
accuracy of the advection scheme rather than increasing the spatial resolution. This is certainly true for the idealized turbulence experiments
they perform, but it is probably not yet true for realistic ocean models. Subgrid scale topographic effects are the reason for this. Refining
the grid offers the opportunity to better represent key straits and passages, which a higher order scheme cannot provide. This is certainly
the reason why most ocean models still use second order, inexpensive
advection schemes. This situation may change in the future, as higher
spatial resolutions are allowed by the computational resources.
5.
Dynamical effects of mesoscale eddies
5.1
Baroclinic instability
Gent and McWilliams (1990), hereafter GM, have noted that parameterizing the mixing of salinity and temperature anomalies on isopycnals
by mesoscale eddies is not enough, because this leaves aside the dynamical effect of eddies on the density field. Most of the eddy energy in the
ocean is believed to arise due to baroclinic instability of the mean flow.
Baroclinically unstable eddies extract available potential energy from the
mean flow, thus tending to flatten isopycnals. The GM parameterizamod
ANNE-MARIE TREGUIER
els it has mainly been used in MICOM (Bleck and Boudra, 1981). A
study by Griffies and Hallberg (2003) suggests that using a biharmonic
operator with Smagorinsky-like viscosity is better in eddy permitting
simulation when the flow is non homogeneous (in the presence of western boundary currents, for instance) because it allows lower levels of
viscosity in the interior.
This short review emphasizes numerical constraints as the basis for
the choice of parameterizations of momentum mixing. We can hope
that more physically based parameterizations will emerge in the future.
Smith and McWilliams (2003) have developed a promising framework
by deriving a general form for anisotropic viscosity, and an elegant functional form for the discretization following a similar work by Griffies
et al. (1998) on the isoneutral diffusion.
For completeness we must mention here another approach to parameterizations. It consists in using the properties of numerical advections
schemes to represent the cascade of enstrophy to small scales (this also
applies to cascade of tracer variance reviewed in the previous section).
With that strategy, no explicit parameterization is needed. Shchepetkin
and McWiliams (1998) advocate this approach, claiming that higher
Reynolds numbers can be simulated that way, compared with the combination of a classical advection scheme and hyperviscosity. Those authors also claim that it is more computationaly efficient to increase the
accuracy of the advection scheme rather than increasing the spatial resolution. This is certainly true for the idealized turbulence experiments
they perform, but it is probably not yet true for realistic ocean models. Subgrid scale topographic effects are the reason for this. Refining
the grid offers the opportunity to better represent key straits and passages, which a higher order scheme cannot provide. This is certainly
the reason why most ocean models still use second order, inexpensive
advection schemes. This situation may change in the future, as higher
spatial resolutions are allowed by the computational resources.
5.
Dynamical effects of mesoscale eddies
5.1
Baroclinic instability
Gent and McWilliams (1990), hereafter GM, have noted that parameterizing the mixing of salinity and temperature anomalies on isopycnals
by mesoscale eddies is not enough, because this leaves aside the dynamical effect of eddies on the density field. Most of the eddy energy in the
ocean is believed to arise due to baroclinic instability of the mean flow.
Baroclinically unstable eddies extract available potential energy from the
mean flow, thus tending to flatten isopycnals. The GM parameterizamod