Publication Abstracts

Canuto 1994

Canuto, V.M., 1994: Large eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy. Astrophys. J., 428, 729-752, doi:10.1086/174281.

The Reynolds numbers that characterize geophysical and astrophysical turbulence (Re ≈ 106 for the planetary boundary layer and Re ≈ 1014 for the Sun's interior) are too large to allow a direct numerical simulation (DNS) of the fundamental Navier-Stokes and temperature equations. In fact, the spatial number of grid points N ∼ Re9/4 exceeds the computational capability of today's supercomputers.

Alternative treatments are the ensemble-time average approach, and/or the volume average approach. Since the first method (Reynolds stress approach) is largely analytical, the resulting turbulence equations entail manageable computational requirements and can thus be linked to a stellar evolutionary code or, in the geophysical case, to general circulation models. In the volume average approach, one carries out a large eddy simulation (LES) which resolves numerically the large scales, while the unresolved scales must be treated theoretically with a subgrid scale model (SGS). Contrary to the ensemble average approach, the LES+SGS approach has considerable computational requirements. Even if this prevents (for the time being) a LES+SGS model to be linked to stellar or geophysical codes, it is still of the greatest relevance as an "experimental tool" to be used, inter alia, to improve the parameterizations needed in the ensemble average approach. Such a methodology has been successfully adopted in studies of the convective planetary boundary layer.

Experience with the LES+SGS approach from different fields has shown that its reliability depends on the healthiness of the SGS model for numerical stability as well as for computational completeness. At present, the most widely used SGS model, the Smagorinsky model, accounts for the effect of the shear induced by the large resolved scales on the unresolved scales but does not account for the effects of buoyancy, anisotropy, rotation, and stable stratification. The latter phenomenon, which affects bnoth geophysical and astrophysical turbulence (e.g., oceanic structure and convective overshooting in stars), has been singularly difficult to account for in turbulence modeling. For example, the widely used model of Deardorff has not been confirmed by recent LES results. As of today, there is no SGS model capable of incorporating buoyancy, rotation, shear, anisotropy, and stable stratification (gravity waves).

In this paper, we construct such a model which we call CM (complete model). We also present a hierarchy of simpler algebraic models (called AM) of varying complexity. Finally, we present a set of models which are simplified even further (called SM), the simplest of which is the Smagorinsky-Lilly model. The incorporation of these models into the presently available LES codes should begin with the SM, to be followed by the AM and finally by the CM.

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BibTeX Citation

@article{ca03900e,
  author={Canuto, V. M.},
  title={Large eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy},
  year={1994},
  journal={Astrophys. J.},
  volume={428},
  pages={729--752},
  doi={10.1086/174281},
}

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RIS Citation

TY  - JOUR
ID  - ca03900e
AU  - Canuto, V. M.
PY  - 1994
TI  - Large eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy
JA  - Astrophys. J.
VL  - 428
SP  - 729
EP  - 752
DO  - 10.1086/174281
ER  -

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