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| Titel |
Nondissipative Velocity and Pressure Regularizations for the ICON Model |
| VerfasserIn |
M. Restelli, M. Giorgetta, T. Hundertmark, P. Korn, S. Reich |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250024099
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| Zusammenfassung |
| A challenging aspect in the numerical simulation of atmospheric and oceanic flows is the
multiscale character of the problem both in space and time. The small spacial scales are
generated by the turbulent energy and enstrophy cascades, and are usually dealt with by
means of turbulence parametrizations, while the small temporal scales are governed by the
propagation of acoustic and gravity waves, which are of little importance for the large scale
dynamics and are often eliminated by means of a semi-implicit time discretization. We
propose to treat both phenomena of subgrid turbulence and temporal scale separation in a
unified way by means of nondissipative regularizations of the underlying model equations.
More precisely, we discuss the use of two regularized equation sets: the velocity
regularization, also know as Lagrangian averaged Navier–Stokes system, and the pressure
regularization. Both regularizations are nondissipative since they do not enhance the
dissipation of energy and enstrophy of the flow. The velocity regularization models the effects
of the subgrid velocity fluctuations on the mean flow, it has thus been proposed as a
turbulence parametrization and it has been found to yield promising results in ocean
modeling [HHPW08]. In particular, the velocity regularization results in a higher variability
of the numerical solution. The pressure regularization, discussed in [RWS07],
modifies the propagation of acoustic and gravity waves so that the resulting system
can be discretized explicitly in time with time steps analogous to those allowed
by a semi-implicit method. Compared to semi-implicit time integrators, however,
the pressure regularization takes fully into account the geostrophic balance of the
flow.
We discuss here the implementation of the velocity and pressure regularizations within
the numerical framework of the ICON general circulation model (GCM)Â [BR05] for the case
of the rotating shallow water system, showing how the original numerical formulation can be
extended to the regularized systems retaining discrete conservation of mass and
potential enstrophy. We also present some numerical results both in planar, doubly
periodic geometry and in spherical geometry. These results show that our numerical
formulation correctly approximates the behavior of the regularized models, and are a first
step toward the use of the regularization idea within a complete, three-dimensional
GCM.
References
[BR05]    L. Bonaventura and T. Ringler. Analysis of discrete shallow-water
models on geodesic Delaunay grids with C-type staggering. Mon. Wea.
Rev., 133(8):2351–2373, August 2005.
[HHPW08]Â Â Â M.W. Hecht, D.D. Holm, M.R. Petersen, and B.A. Wingate.
Implementation of the LANS-α turbulence model in a primitive equation
ocean model. J. Comp. Phys., 227(11):5691–5716, May 2008.
[RWS07]    S. Reich, N. Wood, and A. Staniforth. Semi-implicit methods,
nonlinear balance, and regularized equations. Atmos. Sci. Lett., 8(1):1–6,
2007. |
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