{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T02:13:01Z","timestamp":1787278381316,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>A five-degree model, which reproduces faithfully the sequence of bifurcations and the type of solutions found through numerical simulations of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells with fixed azimuthal symmetry, is derived. A low Prandtl number fluid of $\\sigma=0.1$ subject to radial gravity, filling a shell of radius ratio $\\eta=0.35$, differentially heated, and with non-slip boundary conditions, is considered. Periodic, quasi-periodic, and temporal chaotic flows are obtained for a moderately small Ekman number, $E=10^{-4}$, and at supercritical Rayleigh numbers of order $Ra\\sim O(2Ra_c)$. The solutions are classified by means of frequency analysis and Poincar\u00e9 sections. Resonant phase locking on the quasi-periodic branches, as well as a sequence of period doubling bifurcations, are also detected.<\/jats:p>","DOI":"10.1137\/15m100729x","type":"journal-article","created":{"date-parts":[[2015,10,20]],"date-time":"2015-10-20T13:39:44Z","timestamp":1445348384000},"page":"1787-1807","source":"Crossref","is-referenced-by-count":10,"title":["Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions"],"prefix":"10.1137","volume":"14","author":[{"given":"F.","family":"Garcia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"S\u00e1nchez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Dormy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Net","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,10,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1080\/03091920410001659281"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0031-9201(96)03200-1"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1029\/2002GC000456"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2011.421"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112070001921"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0031-9201(94)90075-2"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"P. Chossat and G. Iooss,\n                      The Couette-Taylor Problem\n                      , Springer-Verlag, New York, 1994.","DOI":"10.1007\/978-1-4612-4300-7"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112002002008"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112003007316"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/19\/3\/005"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.87.023021"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840301"},{"key":"atypb13","unstructured":"F. Garcia,\n                      Thermal Convection in Rotating Spherical Shells\n                      , Ph.D. thesis, Universitat Polite\u0300cnica de Catalunya, Barcelona, Spain, 2012."},{"key":"atypb14","unstructured":"F. Garcia, E. Dormy, J. Sa\u0301nchez, and M. Net,\n                      Two computational approaches for the simulation of fluid problems in rotating spherical shells\n                      , in Proceedings of the 5th International Conference on Computational Methods - ICCM2014, Vol. 1, G. R. Liu and Z. W. Guan, eds., Cambridge, England, 2014."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.07.004"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"F. Garcia, M. Net, and J. Sa\u0301nchez,\n                      A comparison of high-order time integrators for highly supercritical thermal convection in rotating spherical shells\n                      , in Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012, Lect. Notes Comput. Sci. Eng. 95, M. Azai\u0308ez, H. El Fekih, and J. S. 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