Quantification of spurious dissipation
and mixing in ocean models:
discrete variance decay
in a finite-volume framework
Hans Burchard1, Carsten Eden2, Ulf Gräwe1,
Knut Klingbeil1, Mahdi Mohammadi-Aragh1
and Nils Brüggemann2
1. Leibniz Institute for Baltic Sea Research Warnemünde, Germany
2. ClimaCampus, University of Hamburg, Germany
Numerical variance decay of tracers: numerical mixing.
Numerical variance decay of velocity: numerical dissipation.
Method I (Burchard & Rennau, 2008) in a nutshell
Generalisation
by Burchard
& for
Rennau
First-order
(FOU)
s: (2008)
1D advectionupstream
equation
for S:
for any advection scheme:
Numerical mixing is the advected tracer square
minus the square of the advected tracer, divided by Dt.
1D
equation to
forFOU
s2: for s² with variance decay :
FOUadvection
for s is equivalent
numerical diffusivity
Salinity gradient squared
Morales Maqueda & Holloway (2006)
Reconstruct
Method II: Klingbeil et al. (under review), also in a nutshell
Average
Evolve
decomposition
1
recombination
adapted from Morales Maqueda and Holloway (2006)
Comparing methods I & II in 1D
Variance loss due
to recombination
Variance gain due
to decomposition
Klingbeil et al. (under review)
Salinity mixing analysis in Western Baltic Sea
(adaptive coordinates)
Klingbeil et al. (under review)
Meso-scale dynamics and stratification in Eady channel
SST
zonally averaged q
Restratification occurs due to extraction of kinetic energy from
geostrophically balanced flow to eddy kinetic energy (due to momentum advection),
a process which critically depends on numerical mixing and dissipation.
Mohammadi-Aragh et al. (in preparation)
Meso-scale dynamics and stratification in Eady channel
stratification
numerical dissipation
background potential energy
Mohammadi-Aragh et al. (in preparation)
Take home message
Numerical mixing & dissipation are specifically critical in regimes
with low physical mixing & dissipation and strong eddy dynamics.
Accurate methods for the local quantification of numerical mixing
and dissipation have been introduced.
For realistic ocean modelling, good parameterisations of physical
mixing and dissipation need to be combined with accurate advection
schemes and an optimal choice for the numerical grid (isopcynal or
adaptive coordinates help).
To derive new meso-scale or sub-meso-scale mixing parameterisations
using numerical experiments, reference experiments with high numerical
accuracy need to be employed.
All simulations carried out with the
General Estuarine Transport Model (GETM, www.getm.eu)