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Quantitative analysis of numerically induced mixing in a coastal model application. Hannes Rennau and Hans Burchard Baltic Sea Research Institute Warnemünde (IOW). hannes.rennau@io-warnemuende.de. z. y. x. Representing overflows in numerical models. t1: vel.>0
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Quantitative analysis of numerically induced mixing in a coastal model application Hannes Rennau and Hans Burchard Baltic Sea Research Institute Warnemünde (IOW) hannes.rennau@io-warnemuende.de
z y x Representing overflows in numerical models t1: vel.>0 t2: vel.<0 Hydraulic control Tracer detrainment Downslope descent Geostrophic eddies Tracer Shear instability, entrainment terrain-following coordinates Bottom friction vs. discretisation errors of numerical advection schemes some physical processes in overflows hannes.rennau@io-warnemuende.de
Bulk measure for physical mixing physical mixing = turbulent mean tracer variance decay rate 2 DS Dz Mixphy = 2K n -> mixing is dissipation of tracer variance 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] ] hannes.rennau@io-warnemuende.de
GETM (getm.eu) hindcast: hannes.rennau@io-warnemuende.de
Vertically integrated and time-averagedamount of physical mixing hannes.rennau@io-warnemuende.de
Bulk measure for numerical diffusion define for any advection scheme the numerical variance decay as: advection step Burchard, H., and H. Rennau, Comparative quantification of physically and numerically induced mixing in ocean models, Ocean Modelling, 2008, accepted for publication. ] hannes.rennau@io-warnemuende.de
Quantification of numerical diffusion in spatial x-, y- and z-direction physical mixing model domain hannes.rennau@io-warnemuende.de
time-avg. time-avg. time-avg. Quantification of numerical diffusion in spatial x-, y- and w-direction along channel neutral to vert. interfaces cross channel snapshot snapshot snapshot hannes.rennau@io-warnemuende.de
physical diffusion numerical diffusion hannes.rennau@io-warnemuende.de
Vertically integrated and time-averaged amount of physical and numerical diffusion 1.Feb2004 – 12.Feb 2004 hannes.rennau@io-warnemuende.de
time-averaged and vertically integrated physically and numerically induced salinity variance decay Physical mixingNumerical mixing hannes.rennau@io-warnemuende.de
Conclusions generic method – no approximation ! • 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 hannes.rennau@io-warnemuende.de
