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| Titel |
On the use of a depth-dependent barotropic mode for free surface ocean models |
| VerfasserIn |
J. Demange, L. Debreu, P. Marchesiello, E. Blayo |
| 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 |
250070968
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| Zusammenfassung |
| It is well known from the linear theory that the strongest stability constraint on a numerical
ocean model is given by the propagation of the barotropic mode. The rigid lid approximation
removes this constraint at the price of the solution of an elliptic system with barotropic
streamfunction or surface pressure as unknown. In the rigid lid approximation, the barotropic
mode is vertically constant and so the barotropic part of the flow can be identified to the depth
integrated flow.
When, for physical motivations, a free surface is introduced, the modification of the surface
boundary condition renders the barotropic mode slightly non constant [3]. However since the
first introduction of a free surface in an ocean model ([1], [4]), the barotropic mode is still
assumed to be vertically constant in order to simplify the derivation of the barotropic system,
which is then treated either using a time splitting method with small time steps or implicitly
[2].
This assumption has two trade-off effects. First, the loss of orthogonality and aliasing
between the barotropic and baroclinic modes results in the need for filtering [5]
even in the linear case, albeit this is not theoretically required. This filtering can
greatly alter the propagation of several physical signals (e.g. tidal waves). Second,
again due to non orthogonality of the modes, the additional diffusion put on the
approximated barotropic mode also alters the vertical structure of the baroclinic parts of the
flow.
In this presentation, these two issues are illustrated in the case of the propagation of either a
barotropic or baroclinic mode over a flat bottom ocean using linearized primitive equations,
i.e. when the modal decomposition is valid. The continuous approach is recalled and the
discrete implementation of a time splitting scheme based on a depth-dependent barotropic
mode is introduced. This noticeably includes a 3D correction of the density field by its 2D
barotropic counterpart.
The extension to the nonlinear case is obviously non trivial. Nevertheless, we propose to
solve an approximate barotropic system which conforms to the theory when linearized.
Numerical simulations of the propagation of internal gravity waves are showed and
perspectives are drawn.
References
[1]   A. Blumberg and G. Mellor. A description of a three-dimensional coastal
ocean circulation model. In N. Heaps, editor, Three-Dimensional Coastal Ocean
Models, pages 1–16. American Geophys. Union, 1987.
[2]   J. Dukowicz and R. Smith. Implicit free-surface method for the |
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