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| Titel |
Stochastic closure for local averages in a finite difference discretization: an application to the forced/inviscid Burgers equation |
| VerfasserIn |
S. Dolaptchiev, U. Achatz, I. Timofeyev |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250062087
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| Zusammenfassung |
| The development of numerically efficient models for atmospheric flow is a topic of ongoing
research. Need for such models arises wherever the interest is predominantly in the dynamics
of a coarse-grained flow which is, however, interacting with small-scale structures not to be
resolved explicitly. Typical applications are, e.g., the parameterization of meso-scale or
synoptic-scale eddies in large-scale climate models or the treatment of the impact of
small-scale turbulence on the larger turbulent structures in large-eddy simulations. We present
a systematic framework for the development of a stochastic closure for local averages of
various atmospheric quantities. The parameterization is derived from the finite difference
discretization of the full model equations by utilizing stochastic mode reduction
techniques [1]. It includes linear and nonlinear corrections, as well as additive and
multiplicative noise terms. The new parameterization is implemented for the Burgers
equation, where we consider a stochastically forced case as well as the inviscid case. In
order to assess the performance of the closure, it is compared with two benchmark
parameterizations: a Smagorinsky sub-grid scale model and a purely empirical linear
stochastic parameterization. The new parameterization improves the representation of the
inertial energy range (forced case) and higher order statistical moments (inviscid
case).
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 S. Dolaptchiev, U. Achatz, I. Timofeyev, Stochastic closure for local averages
in the finite difference discretization of the Burgers equation, in preparation. |
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