OCEAN MODELS
97
one using a horizontal biharmonic coefficient (like PSY2 and MFS) with
value of 5.5 10 10 m 4 .s −1 at the equator, and the other one using a isopycnal laplacian mixing (like FOAM) with coefficient 200 m 2 .s −1 . Results
were not conclusive. The meridional overturning was enhanced by 2 Sv
with the isopycnal mixing, which was assumed to be an improvement,
but the deep jets analyzed by Treguier et al. (2003) were weaker with
isopycnal mixing and the Agulhas eddies seemed too stable.
To make progress with the parameterization of lateral mixing at the
sub-mesoscale, we need to understand the physical processes better.
Sub-mesoscales are difficult to observe, but high resolution quasi-geostrophic or two-dimensional models give us insights into their behavior. One
key phenomenon in the tracer cascade to small scales is the formation of
elongated filaments, which occurs preferentially at critical points around
the eddies when they interact with each other. This flow structure with
energetic eddy cores surrounded by filaments is found in all high resolution models. Fig. 8 shows an example in the PSY2 model without data
assimilation). Recent studies help understand where and when filaments
form as a function of resolved flow quantities (see for example Klein
et al., 2000). Parameterizations based on such analysis in physical space
(by opposition to the more usual biharmonic or hyperviscosities based
only on the cascade in spectral space) look promising, like the one by
Dubos and Babiano (2002). So far they have not been implemented in
realistic primitive equation models.
If mixing at the submesoscale is mainly performed by the combined
action of vertically sheared inertial oscillations and vertical mixing as
proposed by Young et al. (1982), then a parameterization must include
the effect of mesoscale eddies on the inertial oscillations. Such a parameterization is tested by Klein et al. (2003) in quasi-geostrophic models
and shown to cause an assymetry between anticyclonic and cyclonic
structures.
One important issue that is too often ignored in parameterizations of
isopycnal mixing is the large inhomogeneity of the mesoscale eddy field,
which is now very well mapped from satellite altimetry. Obviously the
isopycnal diffusivity κ in non-eddy resolving model should depend on
the eddy activity. One possible way to achieve that is to use a scaling
based on the time scale for baroclinic instability (Treguier et al., 1997).
Such spatially variable coefficients have been used to represent the dynamical effect of eddies (see next section), but their use for mixing of
tracers along isopycnals is not documented. Note that sharp variations
in the eddy mixing coefficient κ can increase the gradients of tracers
along isopycnals, as shown in Fig. 5. It will also create an advection of
tracers away from the regions of active eddies. This advection is different
97
one using a horizontal biharmonic coefficient (like PSY2 and MFS) with
value of 5.5 10 10 m 4 .s −1 at the equator, and the other one using a isopycnal laplacian mixing (like FOAM) with coefficient 200 m 2 .s −1 . Results
were not conclusive. The meridional overturning was enhanced by 2 Sv
with the isopycnal mixing, which was assumed to be an improvement,
but the deep jets analyzed by Treguier et al. (2003) were weaker with
isopycnal mixing and the Agulhas eddies seemed too stable.
To make progress with the parameterization of lateral mixing at the
sub-mesoscale, we need to understand the physical processes better.
Sub-mesoscales are difficult to observe, but high resolution quasi-geostrophic or two-dimensional models give us insights into their behavior. One
key phenomenon in the tracer cascade to small scales is the formation of
elongated filaments, which occurs preferentially at critical points around
the eddies when they interact with each other. This flow structure with
energetic eddy cores surrounded by filaments is found in all high resolution models. Fig. 8 shows an example in the PSY2 model without data
assimilation). Recent studies help understand where and when filaments
form as a function of resolved flow quantities (see for example Klein
et al., 2000). Parameterizations based on such analysis in physical space
(by opposition to the more usual biharmonic or hyperviscosities based
only on the cascade in spectral space) look promising, like the one by
Dubos and Babiano (2002). So far they have not been implemented in
realistic primitive equation models.
If mixing at the submesoscale is mainly performed by the combined
action of vertically sheared inertial oscillations and vertical mixing as
proposed by Young et al. (1982), then a parameterization must include
the effect of mesoscale eddies on the inertial oscillations. Such a parameterization is tested by Klein et al. (2003) in quasi-geostrophic models
and shown to cause an assymetry between anticyclonic and cyclonic
structures.
One important issue that is too often ignored in parameterizations of
isopycnal mixing is the large inhomogeneity of the mesoscale eddy field,
which is now very well mapped from satellite altimetry. Obviously the
isopycnal diffusivity κ in non-eddy resolving model should depend on
the eddy activity. One possible way to achieve that is to use a scaling
based on the time scale for baroclinic instability (Treguier et al., 1997).
Such spatially variable coefficients have been used to represent the dynamical effect of eddies (see next section), but their use for mixing of
tracers along isopycnals is not documented. Note that sharp variations
in the eddy mixing coefficient κ can increase the gradients of tracers
along isopycnals, as shown in Fig. 5. It will also create an advection of
tracers away from the regions of active eddies. This advection is different