Reduction of numerical mixing
by means of vertically adaptive coordinates in ocean models
Hans Burchard1, Ulf Gräwe1, Richard Hofmeister2, Knut Klingbeil1, Inga Hense3 and Jean-Marie
Beckers4
1. Leibniz Institute for Baltic Sea Research Warnemünde, Germany2. Helmholtz-Zentrum Geesthacht, Institute for Coastal Research,
Germany3. ClimaCampus, University of Hamburg, Germany
4. GHER, University of Liege, Belgium
What is mixing ?Reynolds-averaged salinity equation with downgradient turbulent transport (no horizontal turbulent transport):
Salinity variance equation:
?Mixing is dissipation of tracer variance.
Numerical mixing due to tracer advection can be calculated.Burchard and Rennau (2008)
2 approaches to quantify numerical mixing
A: Compare square of advected tracer with advected tracer square (Burchard & Rennau 2008)
B: Reconstruct tracer transports through individual layer interfaces and quantify the mixing (Maqueda Morales & Holloway 2006; Klingbeil et al. in prep.)
„Baltic Slice“ simulation
Burchard and Rennau (2008)
salinity velocity
numerical mixing physical mixing
Burchard and Rennau (2008)
Adaptive vertical grids in GETM
hor. filteringof layer heightsVertical zooming
of layer interfaces towards:
a) Stratification
b) Shear
c) surface/ bottom
z
bottom
Vertical direction
Horizontal direction
hor. filteringof vertical position
Lagrangiantendency
isopycnaltendency
Solution of a vertical diffusion equation for the coordinate position
Burchard & Beckers (2004); Hofmeister, Burchard & Beckers (2010a)
Burchard & Beckers (2004);
Example for grid adaptation for wind entrainment experiment
Baltic slice with adaptive vertical coordinates
Fixed coordinates Adaptive coordinates
Hofmeister, Burchard & Beckers (2010)
Numerical mixing Numerical mixingPhysical mixing Physical mixing
Salinity mixing analysis in Western Baltic Sea(adaptive coordinates)
Klingbeil et al. (almost submitted)
[°C]
Gräwe et al. (in prep.)
phys & bio adaptive with 50 layers
phys & bio adaptive with 30 layers
phys adaptive with 30 layers
non-adaptive with 30 layers
Temperature transect
Grid adaptation in Northern North Sea(additional adaptation to
biogeochemistry)
phys & bio adaptive with 50 layers
phys & bio adaptive with 30 layers
phys adaptive with 30 layers
non-adaptive with 30 layers
Nutrient transect [mmol N/m3]
Gräwe et al. (in prep.)
Grid adaptation in Northern North Sea(additional adaptation to
biogeochemistry)
ConclusionsIn stratified flow simulations, the numerically induced mixing maybe of the same order or even much larger than the physical mixing.
Vertical coordinate adaptation leads to optimised model resolution in a waythat its additional computational effort is strongly overcompensated by the gain in accuracy.
Vertical coordinate adaptation can also be applied to biogeochemical properties or other tracers (in addition to u & T & S).
Advantages of vertically adaptive coordinates are substantial for shelf seasimulations, but also large scale simulations should profit from this concept.