**Subsections**

#

Conservation Properties on Tracers

All the numerical schemes used in NEMO are written such that the tracer content
is conserved by the internal dynamics and physics (equations in flux form).
For advection, only the CEN2 scheme ( order finite different scheme)
conserves the global variance of tracer. Nevertheless the other schemes ensure
that the global variance decreases ( they are at least slightly diffusive).
For diffusion, all the schemes ensure the decrease of the total tracer variance,
except the iso-neutral operator. There is generally no strict conservation of mass,
as the equation of state is non linear with respect to and . In practice,
the mass is conserved to a very high accuracy.

##

Advection Term

conservation of a tracer, :

conservation of its variance:

Whatever the advection scheme considered it conserves of the tracer content as all
the scheme are written in flux form. Indeed, let be the tracer and , ,
and its interpolated values at velocity point (whatever the interpolation is),
the conservation of the tracer content due to the advection tendency is obtained as follows:

The conservation of the variance of tracer due to the advection tendency
can be achieved only with the CEN2 scheme, when
,
, and
.
It can be demonstarted as follows:

which is the discrete form of
.

Gurvan Madec and the NEMO Team

NEMO European Consortium2017-02-17