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02.04.13: Some notes concerning LANS-α models

  • (Holm et al. 2005, p. 161): Test of LANS-α models focus on reproducing the Eulerian-mean flow from a higher resolution model. I state that 1) we may need to reproduce the Lagrangian-mean flow reproduced in the higher resolution model and 2) this might be possible only by choosing the right values of mixing parameters (who still exist in LAN-α models, see below) based on information coming from outside the model.
  • (Holm et al. 2005, p. 166): GLM equations combined with Taylor closure gives the LAE-α equations (see also Holm 2002).
  • (Holm et al. 2005, p. 157): LANS-α equations tend to Navier-Stokes equations when α goes to zero but only if the viscosity used in the LANS-α model is also the molecular diffusivity. In practice for eddy-resolving models, the viscous terms are also parameterized (biharmonic scheme for the POP-α model; see Hecht et al. 2008, p. 5709) and so the equations do not converge to Navier-Stokes equations in that case.
  • (Hecht et al. 2008b, p. 8): “It is important here to understand that effective use of the POP-α model does not parameterize the effect of eddies, but more readily allows for the inclusion of eddies”.

References:

  • Holm et al. 2005: The LANS-α model for computing turbulence. Los Alamos Science, 29, 152–171.
  • Hecht et al 2008: Implementation of the LANS-α turbulence model in a primitive equation ocean model. J. Computat. Phys., 227, 5691–5716.
  • Hecht et al 2008b: Lateral mixing in the eddying regime and a new broad-ranging formulation. In: Hecht, Hasumi (Eds.), Ocean Modeling in an Eddying Regime. AGU Monograph Series. AGU, pp. 339–352.