96
ANNE-MARIE TREGUIER
4.2
Isopycnal mixing of tracers
Let us consider lateral mixing operators in our eddy permitting models (table 2). Some models use a laplacian operator rotated to follow
the isopycnal (neutral) direction, others use a horizontal biharmonic
(bi-laplacian) operator. The biharmonic operator has been introduced
in quasi-geostrophic models based on the properties of two-dimensional
turbulence. Because it is more scale-selective, it allows a model to represent a larger part of the mesoscale spectrum at a given grid resolution,
while removing variance at the grid scale at a sufficient rate to avoid
grid scale noise. However, the biharmonic operator can cause spurious
overshoots in tracer properties (Mariotti et al., 1994), so that it has disadvantages as well as advantages. The inconveniences are pointed out
in more detail by Griffies (2004).
Examination of the basin-scale water mass properties reveals that they
spread along isopycnals (not horizontally), due to advection and stirring
by mesoscale eddies. Analysis of tracer release experiments (Ledwell
et al., 1998) suggest that mixing is isopycnal down to scales of 100 m, so
that there is no evidence to support the choice of a horizontal mixing
as in PSY2 or MFS. Toole (1998) reviews the processes that may be
responsible for isopycnal mixing at different scales. Shear dispersion
due to near-inertial internal waves can cause an isopycnal diffusivity
of ≈ 0.07 m 2 .s −1 at scales between 100 m and 1 km. Vortical modes
could be responsible for diffusivities of ≈ 2 m 2 .s −1 at scales 1 to 30 km,
and mesoscale eddies can cause diffusivities up to 1000 m 2 .s −1 at scales
larger than 300 km. The eddy resolving models using isopycnal mixing
cannot be run with diffusivities as low as observed; FOAM for example
uses κ = 100 m 2 .s −1 . This large value is needed to avoid numerical
accumulation of enstrophy at the model grid scale (12 km).
From the observations of Ledwell et al. (1998), it seems that isopycnal diffusivities increase roughly linearly with the length scale. This
would justify the choice made by some modellers to make the diffusivity
proportional to the grid scale (or the third power of the grid scale in the
case of a biharmonic operator), as for example in the DYNAMO models
(Willebrand et al., 2001), or in PSY2.
The above considerations would support the choice of a biharmonic
operator (for its scale selectiveness), rotated along isopycnals for consistency with observations. Often though, modellers do not want to pay
the computational cost of rotating the biharmonic. This explains why
the two alternatives found in table 2 are a horizontal biharmonic and an
isopycnal laplacian. Those two parameterizations were compared during
the CLIPPER project. Two experiments were run with the ATL6 model,
ANNE-MARIE TREGUIER
4.2
Isopycnal mixing of tracers
Let us consider lateral mixing operators in our eddy permitting models (table 2). Some models use a laplacian operator rotated to follow
the isopycnal (neutral) direction, others use a horizontal biharmonic
(bi-laplacian) operator. The biharmonic operator has been introduced
in quasi-geostrophic models based on the properties of two-dimensional
turbulence. Because it is more scale-selective, it allows a model to represent a larger part of the mesoscale spectrum at a given grid resolution,
while removing variance at the grid scale at a sufficient rate to avoid
grid scale noise. However, the biharmonic operator can cause spurious
overshoots in tracer properties (Mariotti et al., 1994), so that it has disadvantages as well as advantages. The inconveniences are pointed out
in more detail by Griffies (2004).
Examination of the basin-scale water mass properties reveals that they
spread along isopycnals (not horizontally), due to advection and stirring
by mesoscale eddies. Analysis of tracer release experiments (Ledwell
et al., 1998) suggest that mixing is isopycnal down to scales of 100 m, so
that there is no evidence to support the choice of a horizontal mixing
as in PSY2 or MFS. Toole (1998) reviews the processes that may be
responsible for isopycnal mixing at different scales. Shear dispersion
due to near-inertial internal waves can cause an isopycnal diffusivity
of ≈ 0.07 m 2 .s −1 at scales between 100 m and 1 km. Vortical modes
could be responsible for diffusivities of ≈ 2 m 2 .s −1 at scales 1 to 30 km,
and mesoscale eddies can cause diffusivities up to 1000 m 2 .s −1 at scales
larger than 300 km. The eddy resolving models using isopycnal mixing
cannot be run with diffusivities as low as observed; FOAM for example
uses κ = 100 m 2 .s −1 . This large value is needed to avoid numerical
accumulation of enstrophy at the model grid scale (12 km).
From the observations of Ledwell et al. (1998), it seems that isopycnal diffusivities increase roughly linearly with the length scale. This
would justify the choice made by some modellers to make the diffusivity
proportional to the grid scale (or the third power of the grid scale in the
case of a biharmonic operator), as for example in the DYNAMO models
(Willebrand et al., 2001), or in PSY2.
The above considerations would support the choice of a biharmonic
operator (for its scale selectiveness), rotated along isopycnals for consistency with observations. Often though, modellers do not want to pay
the computational cost of rotating the biharmonic. This explains why
the two alternatives found in table 2 are a horizontal biharmonic and an
isopycnal laplacian. Those two parameterizations were compared during
the CLIPPER project. Two experiments were run with the ATL6 model,