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Comparative Quantification of Mixing in a Coastal Model: Numerical vs. Physical Inductions

Explore the impact of physical and numerical mixing in a coastal model application. Discuss the processes of mixing, including micro-structure salinity variations and tracer variance dissipation. Analyze the influence of advection schemes on salinity variance decay. Discover how numerical mixing affects the decay of salinity variance compared to physical mixing. Considerations for improving mixing formulations in models.

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Comparative Quantification of Mixing in a Coastal Model: Numerical vs. Physical Inductions

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  1. Comparative quantification of physically and numerically induced mixing in a coastal model application Hans Burchard and Hannes Rennau Baltic Sea Research Institute Warnemünde hans.burchard@io-warnemuende.de

  2. What is mixing ? Non-averaged salinity equation: Reynolds decomposition: Mean salinity equation (with down-gradient turbulent flux)

  3. Micro-structure salinity variance equation: Mean salinity variance equation: Mixing is dissipation of tracer variance micro-structure or ensemble-averaged

  4. GETM is a 3D numerical model for estuarine, • coastal and shelf sea hydrodynamics with • Coupling to GOTM Turbulence Module • Generalised vertical coordinates • High-resolution TVD advection schemes • Parallel execution • …

  5. GETM Western Baltic Sea hindcast

  6. Model derived monthly mean vertically integrated salinity variance decay in Western Baltic Sea How does this relate to numerically induced mixing ?

  7. Principle of numerical mixing diagnostics: First-order upstream (FOU) for s: FOU for s is equivalent to FOU for s² with variance decay :

  8. Principle of numerical mixing diagnostics: Reformulation of FOU of s into numerical operator: Reformulation of FOU of s² into operator notation: We define for any advection scheme the numerical variance decay as: Advected tracer square minus square of advected tracer

  9. Loss of salinity2 due to numerical mixing (TVD scheme) Without physical mixing With physical mixing Total salinity squared Loss of salinity squared

  10. Physical and numerical diffusion for the DOME testcase

  11. Numerical mixing Model derived monthly mean vertically integrated physically and numerically induced salinity variance decay Physical mixing

  12. Numerical mixing is not our friend ! Conclusions In buoyancy driven currents, the numerically induced mixing may be of the same order or even much larger than the physical mixing due to entrainment (at least in GETM). The amount of tracer variance is limited. Physics & numerics compete for decaying it. Less numerical mixing allows for more physical mixing. Improved mixing formulations may not result in improved estimates of effective mixing. In order to assess the generality of this problem (for other models than GETM), the analysis of numerically and physically induced tracer squared decay needs to be carried out for many other applications, advection schemes and models.

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