1. 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 hannes.rennau@io-warnemuende.de

2. 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-following coordinates Tracer t1:vel.>0 t2:vel.<0 hannes.rennau@io-warnemuende.de Tracer

3. 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 Mix phy = DS Dz 2K 2 hannes.rennau@io-warnemuende.de

4. PECS 2008, Liverpool GETM (getm.eu) hindcast: hannes.rennau@io-warnemuende.de

5. PECS 2008, Liverpool GETM (getm.eu) hindcast Aug. 2003 – Dec. 2006

6. PECS 2008, Liverpool Vertically integrated and time-averaged amount of physical mixing hannes.rennau@io-warnemuende.de

7. 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 hannes.rennau@io-warnemuende.de

8. PECS 2008, Liverpool Quantification of numerical diffusion in spatial x-, y- and z-direction model domain physical mixing hannes.rennau@io-warnemuende.de

9. PECS 2008, Liverpool Quantification of numerical diffusion in spatial x-, y- and w-direction along channel cross channel neutral to vert. interfaces hannes.rennau@io-warnemuende.de time-avg. time-avg. time-avg. snapshot snapshot snapshot

10. PECS 2008, Liverpool physical diffusion numerical diffusion hannes.rennau@io-warnemuende.de

11. PECS 2008, Liverpool hannes.rennau@io-warnemuende.de Vertically integrated and time-averaged amount of physical and numerical diffusion 1.Feb2004 – 12.Feb 2004

12. PECS 2008, Liverpool time-averaged and vertically integrated physically and numerically induced salinity variance decay Physical mixing Numerical mixing hannes.rennau@io-warnemuende.de

13. 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 ! hannes.rennau@io-warnemuende.de