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| Titel |
A conservative method for hydrostatic flow in isentropic coordinates |
| VerfasserIn |
B. Peeters, O. Bokhove, J. Frank |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250044709
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| Zusammenfassung |
| Although our climate is ultimately driven by (nonuniform) solar heating, many aspects of the
flow can
be understood qualitatively from forcing-free and frictionless dynamics. In the limit of zero
forcing
and dissipation, our weather system falls under the realm of Hamiltonian fluid dynamics and
the flow
conserves potential vorticity (PV), energy and phase-space structure.
We have found a conservative numerical scheme for a hydrostatic atmosphere based on a
mixed
Eulerian-Lagrangian approach, the so-called parcel formulation [1]. For adiabatic flow, the
entropy
is materially conserved. Under stable stratifications, we introduce isentropic coordinates to
simplify the
governing equations. The entropic direction is discretized using finite elements. The
discretization of
horizontal Lagrangian label space (from infinitesimal fluid parcels to discrete fluid particles)
yields a
discrete Poisson bracket. New is that we apply the Hamiltonian Particle-Mesh method [2],
and view
the potential as an Eulerian function, reconstructed from the particle data. The use of an
Eulerian grid
makes the method more efficient and stable. The Hamiltonian consists of a Lagrangian
kinetic energy
and an Eulerian potential energy. The discrete system of ODE’s is thus a Hamiltonian system
conserving
mass, PV, energy and phase-space structure. If we incorporate a symplectic time integrator,
the
resulting fully discrete system conserves energy approximately without any drift in
energy.
Several challenging (nonlinear) solutions will be tested, such a flow over a rising bump. Also,
preliminary
results for bottom-intersecting isentropes will be demonstrated.
REFERENCES
[1] O. Bokhove and M. Oliver, Parcel Eulerian-Lagrangian fluid dynamics for rotating
geophysical
flows, Proc. Roy. Soc. A. 462, pp. 2563-2573 (2006)
[2] J. Frank, G. Gottwald, S. Reich, A Hamiltonian particle-mesh method for the
rotating
shallow-water equations, Lecture Notes in Computational Science and Engineering,
Vol.
26, Springer, Heidelberg, pp. 131-142 (2002) |
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