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| Titel |
Subgrid scale closure for the Burgers equation based on stochastic mode reduction |
| VerfasserIn |
Stamen Dolaptchiev, Ilya Timofeyev, Ulrich Achatz |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250052971
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| Zusammenfassung |
| Applying a systematic stochastic mode reduction strategy [1], a local closure for the subgrid
scale dynamics in the inviscid Burgers equation is constructed. Using an energy and
momentum conserving finite difference discretization and introducing a fine and a coarse
grid, the model variables are split into fast and slow modes. This is a different approach
compared to previous studies, where the separation between the modes is done by truncation
in EOF or Fourier space [2,3]. First, the closure assumptions for the stochastic mode
reduction strategy are verified. Next, an effective stochastic model for the dynamics of the
slow modes is presented. The model performs well in reproducing the variance
and the autocorrelation function of the full model. The contributions of different
terms in the subgrid scale model are analyzed. The application of the approach
to the case, when forcing and dissipation are included in the Burgers equation, is
discussed.
References
[1]Â Â Â A. Majda, I. Timofeyev, E. Vanden-Eijnden, A mathematical framework for
stochastic climate models, Commun. Pure Appl. Math. (2001), 0891-0974.
[2]Â Â Â A. Majda, I. Timofeyev, E. Vanden-Eijnden, A priori tests of a stochastic
mode reduction strategy, Physica D 170 (2002), 206-252.
[3]Â Â Â C. Franzke and A. Majda, Low-Order stochastic mode reduction for a
prototype atmospheric GCM, J. Atmos. Sci 63 (2006), 457-479. |
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