Download - Reduction of numerical mixing by means of vertically adaptive coordinates in ocean models
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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
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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)
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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.)
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„Baltic Slice“ simulation
Burchard and Rennau (2008)
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salinity velocity
numerical mixing physical mixing
Burchard and Rennau (2008)
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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)
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Burchard & Beckers (2004);
Example for grid adaptation for wind entrainment experiment
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Baltic slice with adaptive vertical coordinates
Fixed coordinates Adaptive coordinates
Hofmeister, Burchard & Beckers (2010)
Numerical mixing Numerical mixingPhysical mixing Physical mixing
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Salinity mixing analysis in Western Baltic Sea(adaptive coordinates)
Klingbeil et al. (almost submitted)
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[°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)
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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)
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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.