A. C. Aguilar, P. L. Read, R. D. Wordsworth, T. Salter, and Y. H. Yamazaki, A laboratory model of saturn's north polar hexagon, Icarus, vol.206, issue.2, pp.755-763, 2010.

M. Allison, D. A. Godfrey, and R. F. Beebe, A Wave Dynamical Interpretation of Saturn's Polar Hexagon, Science, vol.247, issue.4946, pp.1061-1063, 1990.
DOI : 10.1126/science.247.4946.1061

A. Antunano, T. Del-rio-gaztelurrutia, A. Sanchez-lavega, and R. Hueso, Dynamics of Saturn's polar regions, Journal of Geophysical Research: Planets, vol.111, issue.2, pp.155-176, 2015.
DOI : 10.1029/2005JE002563

K. H. Baines, T. W. Momary, L. N. Fletcher, A. P. Showman, M. Roos-serote et al., Saturn's north polar cyclone and hexagon at depth revealed by Cassini/VIMS, Planetary and Space Science, vol.57, issue.14-15, pp.14-15, 2009.
DOI : 10.1016/j.pss.2009.06.026

R. Bergmann, L. Tophoj, T. Homan, P. Hersen, A. Andersen et al., Polygon formation and surface flow on a rotating fluid surface, Journal of Fluid Mechanics, vol.679, pp.415-431, 2011.
DOI : 10.1007/978-3-7091-2602-8

F. Bouchut, Chapter 4 Efficient Numerical Finite Volume Schemes for Shallow Water Models, Nonlinear Dynamics of Rotating Shallow 26, 2007.
DOI : 10.1016/S1574-6909(06)02004-1

F. Bouchut, J. Lambaerts, G. Lapeyre, and V. Zeitlin, Fronts and nonlinear waves in a simplified shallow-water model of the atmosphere with moisture and convection, Physics of Fluids, vol.112, issue.11, pp.116604-116604, 2009.
DOI : 10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2

J. P. Boyd, Orthogonal rational functions on a semi-infinite interval, Journal of Computational Physics, vol.70, issue.1, pp.63-88, 1987.
DOI : 10.1016/0021-9991(87)90002-7

T. E. Dowling, Dynamics of Jovian Atmospheres, Annual Review of Fluid Mechanics, vol.27, issue.1, pp.293-334, 1995.
DOI : 10.1146/annurev.fl.27.010195.001453

D. Godfrey, A hexagonal feature around Saturn's north pole, Icarus, vol.76, issue.2, pp.335-356, 1988.
DOI : 10.1016/0019-1035(88)90075-9

D. A. Gurnett, A. M. Persoon, W. S. Kurth, J. B. Groene, T. F. Averkamp et al., The Variable Rotation Period of the Inner Region of Saturn's Plasma Disk, Science, vol.316, issue.5823, pp.442-445, 2007.
DOI : 10.1126/science.1138562

R. Helled, E. Galanti, and Y. Kaspi, Saturn?s fast spin determined from its gravitational field and oblateness, Nature, vol.132, issue.7546, pp.202-204, 2015.
DOI : 10.1051/0004-6361/201118141

URL : http://arxiv.org/abs/1504.02561

T. R. Jansson, M. P. Haspang, K. H. Jensen, P. Hersen, and T. Bohr, Polygons on a Rotating Fluid Surface, Physical Review Letters, vol.4, issue.17, p.174502, 2006.
DOI : 10.1146/annurev.fl.25.010193.001325

URL : http://arxiv.org/abs/physics/0511251

N. Lahaye and V. Zeitlin, Centrifugal, barotropic and baroclinic instabilities of isolated ageostrophic anticyclones in the two-layer rotating shallow water model and their nonlinear saturation, Journal of Fluid Mechanics, vol.21, pp.5-34, 2015.
DOI : 10.1175/1520-0485(2003)033<1197:SOMOVA>2.0.CO;2

J. Lambaerts, G. Lapeyre, and V. Zeitlin, Moist versus Dry Barotropic Instability in a Shallow-Water Model of the Atmosphere with Moist Convection, Journal of the Atmospheric Sciences, vol.68, issue.6, pp.1234-1252, 2011.
DOI : 10.1175/2011JAS3540.1

URL : https://hal.archives-ouvertes.fr/hal-01119312

J. Liu and T. Schneider, Scaling of Off-Equatorial Jets in Giant Planet Atmospheres, Journal of the Atmospheric Sciences, vol.72, issue.1, pp.389-408, 2015.
DOI : 10.1175/JAS-D-13-0391.1

P. S. Marcus and C. Lee, A model for eastward and westward jets in laboratory experiments and planetary atmospheres, Physics of Fluids, vol.249, issue.6, 1998.
DOI : 10.1063/1.868929

R. Morales-juberias, K. M. Sayanagi, T. E. Dowling, and A. P. Ingersoll, Emergence of polar-jet polygons from jet instabilities in a Saturn model, Icarus, vol.211, issue.2, pp.1284-1293, 2011.
DOI : 10.1016/j.icarus.2010.11.006

R. Morales-juberias, K. M. Sayanagi, A. A. Simon, L. N. Fletcher, and R. G. Cosentino, MEANDERING SHALLOW ATMOSPHERIC JET AS A MODEL OF SATURN?S NORTH-POLAR HEXAGON, The Astrophysical Journal, vol.806, issue.1, p.18, 2015.
DOI : 10.1088/2041-8205/806/1/L18

O. Neill, M. E. Emanuel, K. A. Flierl, and G. R. , Weak jets and strong cyclones: Shallow-water modeling of giant planet polar caps, Journal of the Atmospheric Sciences, vol.73, issue.4, pp.1841-1855, 2016.

P. Read, B. Conrath, L. Fletcher, P. Gierasch, A. Simon-miller et al., Mapping potential vorticity dynamics on saturn: Zonal mean circulation from Cassini and Voyager data, Planetary and Space Science, vol.57, issue.14-15, pp.14-15, 2009.
DOI : 10.1016/j.pss.2009.03.004

P. L. Read, T. E. Dowling, and G. Schubert, Saturn???s rotation period from its atmospheric planetary-wave configuration, Nature, vol.299, issue.7255, pp.608-610, 2009.
DOI : 10.1038/nature08194

P. Ripa, General stability conditions for a multi-layer model, Journal of Fluid Mechanics, vol.16, issue.-1, 1990.
DOI : 10.1016/0375-9601(83)90534-0

M. Rostami and V. Zeitlin, -plane model, Geophysical & Astrophysical Fluid Dynamics, vol.112, issue.1, pp.1-31, 2017.
DOI : 10.1175/1520-0469(2001)058<0283:ACOCAS>2.0.CO;2

URL : https://hal.archives-ouvertes.fr/inria-00074650

A. Sanchez-lavega, J. Lecacheux, F. Colas, and P. Laques, Ground-Based Observations of Saturn's North Polar Spot and Hexagon, Science, vol.369, issue.5032, pp.329-332, 1993.
DOI : 10.1086/185956

K. Sayanagi, K. Baines, L. Dyudina, L. Fletcher, A. Sanchez-lavega et al., Saturn's Polar Atmosphere, 2016.

R. K. Scott and L. M. Polvani, Equatorial superrotation in shallow atmospheres, Geophysical Research Letters, vol.50, issue.24, 2008.
DOI : 10.1007/978-94-011-4778-1_134

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.357.2739

A. P. Showman, Numerical Simulations of Forced Shallow-Water Turbulence: Effects of Moist Convection on the Large-Scale Circulation of Jupiter and Saturn, Journal of the Atmospheric Sciences, vol.64, issue.9, pp.3132-3157, 2007.
DOI : 10.1175/JAS4007.1

A. Sánchez-lavega, T. Del-río-gaztelurrutia, R. Hueso, S. Pérez-hoyos, E. García-melendo et al., The long-term steady motion of Saturn's hexagon and the stability of its enclosed jet stream under seasonal changes, Geophysical Research Letters, vol.98, issue.1, pp.1425-1431, 2014.
DOI : 10.1029/2010GL045796

L. N. Trefethen, Spectral methods in matlab, 2000.
DOI : 10.1137/1.9780898719598

A. Vasavada, S. Horst, M. Kennedy, A. Ingersoll, C. C. Porco et al., Cassini imaging of Saturn: Southern hemisphere winds and vortices, Journal of Geophysical Research, vol.135, issue.1, p.5004, 2006.
DOI : 10.1029/2005JE002563

URL : https://trs.jpl.nasa.gov/bitstream/2014/40368/1/06-0106.pdf

G. H. Vatistas, J. Wang, and S. Lin, Recent findings on Kelvin's equilibria, Acta Mechanica, vol.29, issue.1-4, pp.89-102, 1994.
DOI : 10.1007/BF01180220