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PECS 2008, Liverpool
Hannes Rennau and Hans Burchard
Baltic Sea Research Institute Warnemünde (IOW)
Quantitative analysis of numerically induced
mixing in a coastal model application
PECS 2008, Liverpool
Representing overflows in numerical models
discretisation errors of numerical
advection schemes
Shear instability, entrainment
detrainment
Geostrophic eddies
x
z
y
Downslope descent
Bottom friction
some physical processes in overflows
Hydraulic control
vs.
terrain-followingcoordinates
Tracer
t1: vel.>0t2: vel.<0
Tracer
PECS 2008, Liverpool
Bulk measure for physical mixing
physical mixing = turbulent mean tracer variance decay rate
H. Burchard, F. Janssen, K. Bolding, L. Umlauf, and H. Rennau, “Model simulations of
dense bottom currents in the Western Baltic Sea,” Cont. Shelf Res.,
2007. Accepted.Burchard et al. 2008] ]
-> mixing is dissipation of tracer variance
Mixphy =DSDz
2K
2
PECS 2008, Liverpool
GETM (getm.eu) hindcast
Aug. 2003 – Dec. 2006
PECS 2008, Liverpool
Vertically integrated and time-averaged
amount of physical mixing
PECS 2008, Liverpool
Bulk measure for numerical diffusion
]
define for any advection scheme the numerical variance decay as:
Burchard, H., and H. Rennau, Comparative quantification of physically and
numerically induced mixing in ocean models, Ocean Modelling, 2008, accepted for publication.
advection step
PECS 2008, Liverpool
Quantification of numerical diffusion in spatial x-, y- and z-direction
model domain
physical mixing
PECS 2008, Liverpool
Quantification of numerical diffusion in spatial x-, y- and w-direction
along channel cross channel neutral to vert. interfaces
time-avg. time-avg. time-avg.
snapshot snapshot snapshot
PECS 2008, Liverpool
Vertically integrated and time-averaged amount of
physical and numerical diffusion 1.Feb2004 – 12.Feb 2004
PECS 2008, Liverpool
time-averaged and vertically integrated physically and numerically induced salinity variance decay
Physical mixing Numerical mixing
PECS 2008, Liverpool
Conclusions
• numerically induced mixing and physical mixing have same orders of magnitude but different horizontal and vertical distribution
• less numerical mixing –> more physical mixing and vice versa (seen for FCT compared to Superbee/P2 PDM).
• Improve physical mixing formulations, use adaptive vertival coordinates, horizontal/vertical resolution
generic method – no approximation !
