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Quantification of Numerical and Physical Mixing in Coastal Ocean Model Applications

  • Chapter
Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 120))

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Abstract

In this study, the method of numerical mixing analysis is presented for three-dimensional ocean models with general vertical coordinates. Numerical mixing of a scalar is defined as the decay of the square of the scalar due to the three-dimensional advection discretisation. It is shown that for any advection scheme the numerical mixing can be calculated as the difference between the advected square of the scalar and the square of the advected tracer, divided by the time step. Special emphasis on directional-split advection schemes is made. It is shown that for those directional-split schemes the numerical analysis method is exact only when the involved advection of the square of the scalar is carried out individually for each split step. As applications, an idealised meso-scale eddy test scenario without any explicit mixing is calculated. It is shown that only for high-order advection schemes for the scalar (salinity in that case) and the momentum, a physically reasonable solution is obtained. Finally, the method is demonstrated for a fully realistic application to the dynamics of the Western Baltic Sea. Here it becomes clear that physical and numerical mixing depend on each others (increased physical mixing leads to decreased numerical mixing) with the dynamically most relevant mixing being the effective mixing, i.e., the sum of the physical and the numerical mixing.

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Authors and Affiliations

  1. Leibniz Institute for Baltic Sea Research Warnemünde, Seestraße 15, D-18119, Rostock, Germany

    Hans Burchard & Ulf Gräwe

Authors
  1. Hans Burchard
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  2. Ulf Gräwe
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Correspondence to Hans Burchard .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Rainer Ansorge

  2. , Department of Aerospace Engineering, Delft University of Technology, Delft, 2600, Netherlands

    Hester Bijl

  3. , Department of Mathematics and Natural Sc, University of Kassel, Heinrich-Plett-Str. 40, Kassel, 34132, Germany

    Andreas Meister

  4. Institute for Computational Mathematics, Technical University of Braunschweig, Pockelstr. 14, Braunschweig, 38106, Germany

    Thomas Sonar

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Burchard, H., Gräwe, U. (2013). Quantification of Numerical and Physical Mixing in Coastal Ocean Model Applications. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

  • Online ISBN: 978-3-642-33221-0

  • eBook Packages: EngineeringEngineering (R0)

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