Blanc SIMI 1 - Sciences de l'information, de la matière et de l'ingénierie : Mathématiques et interactions

Application of multi-layer rotating shallow water equations for modelling large-scale geophysical and astrophysical flows – SVEMO

SVEMO

Application of multi-layer rotating shallow water equations for modeling large-scale geophysical and astrophysical flows

To construct and to test new reliable and efficient tools for modelling large-scale geo- and astrophysical flows

Main challenge: improving dynamical cores of the general circulation models (atmosphere and ocean).<br /><br />Main goals: construction of efficient numerical schemes for shallow-water equations on the rotating sphere, including «non-standard« terms. Management of date produced by such models. Inclusion of the dynamical effects of moisture in such models . Application for modeling large-scale atmospheric, oceanic and astrophysical phenomena.

Finite-volume well-balanced schemes for rotating shallow water equations with topography with hydrostatic reconstruction. Icosahedral/hexagonal grids on the sphere. Modeling of the moist convection by relaxation schemes and sources/sinks in the multi-layer rotating shallow water equations.

Task 1. «Non-standard« shallow water equations are obtained on the rotating sphere without neglecting any component of the Coriolis force. The role of «non-standard« corrections in destabilizations of jets is quantified.
Task 2. A universal, valid for all grids on the sphere, finite-volume well-balanced scheme is constructed for shallow water equations with topography on the rotating sphere
Task 3. new advection schemes for icosahedral/hexagonal grids are derived. Viewer of the data given on the unstructured grids on the sphere is constructed. A prototype of dynamical cores of the GCM for icosahedral/hexagonal grid is proposed.
Task 4. A new tool: moist-convective multi-layer rotating shallow water model is built and studied. It reproduces with high fidelity the processes observed during the evolution of the atmospheric systems. New coherent structures: ageostrophic modons and tripoles and shock-modons are discovered in rotating shallow water systems. The link between inertial and baroclinic instability is elucidated in the 2-layer model.

To finish successfully the project in 18 months

1.J. Lambaerts, G. Lapeyre and V. Zeitlin, Moist vs dry barotropic instability in a shallow water model of the atmosphere with moist convection, 2011, J. Atmos Sci., 68, 1234-1252.
2.G. Reznik and V. Zeitlin, Resonant excitation of trapped coastal waves by free waves, 2011, J. Fluid Mech. 673, 349-394.
3. J. Lambaerts, G. Lapeyre, V. Zeitlin and F. Bouchut, Simplified two-layer models of
precipitating atmosphere and their properties, 2011, Phys. Fluids, 23, 046603-1 – 046603-24.
4. N. Lahaye and V. Zeitlin, Collisions of ageostrophic modons and formation of new types of coherent structures in rotating shallow water model, 2011, Phys. Fluids, 23, 06173-1 – 06173-4.
5.F. Bouchut, B. Ribstein and V. Zeitlin, Inertial, baroclinic and barotropic instabilities of the Bickley jet in two-layer rotating shallow water model, 2011, Phys. Fluids, 23, 126601-1 – 126601-22.
6.N. Lahaye and V. Zeitlin, Shock-modon: a new type of coherent structure in rotating shallow water, 2012, Phys. Rev. Lett., 108, 044502-1 -- 044502-4.
7.J. Lambaerts, G. Lapeyre and V. Zeitlin, Moist vs dry baroclinic instability in a simplified two-layer atmospheric model with condensation and latent heat release, 2012, J. Atmos. Sci., 69, 1405 -- 1426
8.N. Lahaye and V. Zeitlin, Existence and properties of ageostrophic modons and vortex multipoles in the two-layer shallow water model on the f-plane, 2012, J. Fluid Mech - à paraître, publié en ligne doi:10.1017/jfm.2012.222
9.B. Ribstein and V. Zeitlin, Instabilities of coupled density fronts and their nonlinear evolution in the two-layer rotating shallow water model. Influence of the lower layer and topography, 2012, J. Fluid Mech. - en révision favorable

The goal of the present project is to construct and to test new, reliable and efficient tools for modelling large-scale geo- and astrophysical flows, on the basis of RSW equations, including applications to a new dynamical core of the LMDZ models.
We will:
1.obtain the RSW equations with topography in spherical geometry in systematic fashion by vertical averaging and mean-field approximation; analyse corrections with respect to the « standard » model,
2.develop well-balanced finite-volume numerical scheme(s) for spherical one- and multi-layer RSW equations, both « standard » and with « non-standard » corrections, with first simplified, then realistic topography, and test them on typical test-cases used for GCMs,
3.adapt thus obtained numerical schemes to intensive computations, particularly to massively parallel computing; develop appropriate procedures of dataflow treatment, projections onto alternative grids, and visualizations,
4. obtain the generalizations of the multi-layer RSW to include: convection/precipitation (mRSW), variable density/temperature (rRSW), magnetic field (mhdRSW), and develop corresponding numerical schemes,
5.apply thus obtained models for studies of atmospheric, oceanic and astrophysical processes.

Project coordination

Vladimir ZEITLIN (CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR OUEST ET NORD) – zeitlin@lmd.ens.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Shirshov P.P. Shirshov Institute of Oceanology, Moscou, Russie
LSCE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR SUD
LAMA UNIVERSITE PARIS-EST MARNE LA VALLEE
LMD CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR OUEST ET NORD

Help of the ANR 135,000 euros
Beginning and duration of the scientific project: - 36 Months

Useful links

Explorez notre base de projets financés

 

 

ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter