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On the mathematical stability of stratified flow models with local turbulence closure schemes

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Deleersnijder, Eric [UCL] Hanert, Emmanuel [UCL] Burchard, Hans [Leibniz Institute for Baltic Sea Research Warnemünde] Dijkstra, Henk A. [Institute for Marine and Atmospheric research Utrecht]

Occasionally, numerical simulations using local turbulence closure schemes to estimate vertical turbulent fluxes exhibit small-scale oscillations in space, causing the eddy coefficients to vary over several orders of magnitude on short distances. Theoretical developments suggest that these spurious oscillations are essentially due to the way the eddy coefficients depend on the vertical gradient of the model's variables. An instability criterion is derived based on the assumptions that the artefacts under study are due to the development of small-amplitude, small time- and space-scale perturbations of a smooth solution. The relevance of this criterion is demonstrated by applying it to a series a closure schemes, ranging from the Pacanowski-Philander formulas to the Mellor-Yamada level 2.5 model.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2008
Language Anglais
Journal information "Ocean Dynamics : theoretical, computational oceanography and monitoring" - Vol. 58, no. 3-4, p. 237-246 (2008)
Peer reviewed yes
Publisher Springer Heidelberg (Heidelberg)
issn 1616-7341
e-issn 1616-7228
Publication status Publié
Affiliations UCL - FSA/MECA - Département de mécanique
UCL - AGRO/MILA - Département des sciences du milieu et de l'aménagement du territoire
Keywords Marine modelling ; Vertical mixing ; Turbulence closure ; Stability
Links
  1. Blanke B, Delecluse P (1993) Variability of tropical atlantic ocean simulated by a general circulation model with two different mixed-layer physics. J Phys Oceanogr 23:1363–1388
  2. Brown PS, Pandolfo JP (1982) A numerical predictability problem in solution of the nonlinear diffusion equation. Mon Weather Rev 110:1214–1223
  3. Burchard H (2002a) Applied turbulence modelling in marine waters. No. 100 in Lecture Notes in Earth Science. Springer, Heidelberg
  4. Burchard H (2002b) Energy-conserving discretization of turbulent shear and buoyancy production. Ocean Model 4:347–361
  5. Burchard H, Deleersnijder E (2001) Stability of algebraic non-equilibrium second-order closure models. Ocean Model 3:33–50
  6. Canuto VM, Howard A, Cheng Y, Dubovikov MS (2001) Ocean turbulence. Part I: one point closure model. Momentum and heat vertical diffusivities. J Phys Oceanogr 31:1413–1426
  7. Davies AM, Jones JE (1991) On the numerical solution of the turbulence energy equations for wave and tidal flows. Int J Numer Methods Fluids 12:17–41
  8. Davies HC (1983) The stability of some planetary boundary layer diffusion equations. Mon Weather Rev 111:2140–2143
  9. Deleersnijder E, Burchard H (2003) Reply to Mellor’s comments on “Stability of algebraic non-equilibrium second-order closure models” by H. Burchard and E. Deleersnijder (Ocean Model 3:33–50 (2001)). Ocean Model 5:291–293
  10. Deleersnijder E, Luyten P (1994) On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling. Appl Math Model 18:281–287
  11. Galperin B, Kantha LH, Hassid S, Rosati S (1988) A quasi-equilibrium turbulent energy model for geophysical flows. J Atmos Sci 45:55–62
  12. Girard C, Delage Y (1990) Stable schemes for nonlinear vertical diffusion in atmospheric circulation models. Mon Weather Rev 118:737–745
  13. Goosse H, Deleersnijder E, Fichefet T, England MH (1999) Sensitivity of a global coupled ocean-sea ice model to the parametrisation of vertical mixing. J Geophys Res 104:13681–13695
  14. Hassid S, Galperin B (1983) A turbulent energy model for geophysical flows. Bound Layer Meteorol 26:397–412
  15. Kato H, Phillips OM (1969) On the penetration of a turbulent layer into stratified fluid. J Fluid Mech 37:643–655
  16. Kranenburg C (1980) On the stability of turbulent density-stratified shear flows. J Phys Oceanogr 10:1131–1133
  17. Kranenburg C (1982) Stability conditions for gradient-transport models of turbulent density-stratified shear flows. Geophys Astrophys Fluid Dyn 19:93–104
  18. Mellor GL (2003) Comments on “Stability of algebraic non-equilibrium second-order closure models” by H. Burchard and E. Deleersnijder (Ocean Model 3:33–50 (2001)). Ocean Model 5:193–194
  19. Mellor GL, Yamada T (1974) A hierarchy of turbulence closure models for planetary boundary layers. J Atmos Sci 31:1791–1806
  20. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluids problems. Rev Geophys Space Phys 20:851–875
  21. Munk WH, Anderson ER (1948) Notes on a theory of the thermocline. J Mar Res 3:276–295
  22. Pacanowski RC, Philander SGH (1981) Parametrization of vertical mixing in numerical models of tropical oceans. J Phys Oceanogr 11:1443–1451
  23. Phillips OM (1972) Turbulence in a strongly stratified fluid—is it unstable? Deep Sea Res 19:79–81
  24. Rodi W (1987) Examples of calculation methods for flow and mixing in stratified fluids. J Geophys Res 92(C5):5305–5328
  25. Ruddick KG, Deleersnijder E, Luyten PJ, Ozer J (1995) Haline stratification in the Rhine-Meuse freshwater plume: a three-dimensional model sensitivity analysis. Cont Shelf Res 15:1597–1630
  26. Yamada T (1977) A numerical experiment on pollutant dispersion in a horizontally-homogeneous atmospheric boundary layer. Atmos Environ 11:1015–1024
Bibliographic reference Deleersnijder, Eric ; Hanert, Emmanuel ; Burchard, Hans ; Dijkstra, Henk A.. On the mathematical stability of stratified flow models with local turbulence closure schemes. In: Ocean Dynamics : theoretical, computational oceanography and monitoring, Vol. 58, no. 3-4, p. 237-246 (2008)
Permanent URL http://hdl.handle.net/2078.1/36255