Aj. Weaver et M. Eby, ON THE NUMERICAL IMPLEMENTATION OF ADVECTION SCHEMES FOR USE IN CONJUNCTION WITH VARIOUS MIXING PARAMETERIZATIONS IN THE GFDL OCEAN MODEL, Journal of physical oceanography, 27(2), 1997, pp. 369-377
The results from ocean model experiments conducted with isopycnal and
isopycnal thickness diffusion parameterizations for subgrid-scale mixi
ng associated with mesoscale eddies are examined from a numerical stan
dpoint. It is shown that when the mixing tensor is rotated, so that mi
xing is primarily along isopycnals, numerical problems may occur and n
on-monotonic solutions, which violate the second law of thermodynamics
, may arise when standard centered difference advection algorithms are
used. These numerical problems can be reduced or eliminated if suffic
ient explicit (unphysical) background horizontal diffusion is added to
the mixing scheme. A more appropriate solution is the use of more sop
histicated numerical advection algorithms, such as the flux corrected
transport algorithm. This choice of advection scheme adds additional m
ixing only where it is needed to preserve monotonicty and so retains t
he physically desirable aspects of the isopycnal and isopycnal thickne
ss diffusion parameterizations, while removing the undesirable numeric
al noise. The price for this improvement is a computational increase.