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Climate and Geophysical Fluid Dynamics

The study in geophysical fluid dynamics focuses on two general areas. One area of research is on the study of general circulation models. The other area studies specific physical phenomena. This research program was initiated in early 90's in collaboration with Jacques-Louis Lions and Roger Temam, and has been expanded through collaborations with active geophysicists such as Michael Ghil, Roger Samelson and Kayo Ide.

A. General Circulation Models

[61] Dynamic Bifurcation and Stability in the Rayleigh-B\'enard Convection, submitted, 2003 (with T. Ma)

[54] Hopf Bifurcation in Quasi-Geostrophic Channel Flow, SIAM J. Applied Math., 64:1(2004), 343-368 (with Z. Chen, M. Ghil and E. Simonnet).

[52] Attractor bifurcation theory and its applications to Rayleigh-B\'enard convection, Communications on Pure and Applied Analysis, 2:4(2003), 591--599 (with T. Ma)

[50] Surface Pressure Poisson Equation Formulation of the Primitive Equations: Numerical Schemes, SIAM J. Num. Anal., 41:3(2003), 1163-1194 (with R. Samelson, R. Temam and C. Wang).

[49] Low-Frequency Variability in Shallow Water Models of the Wind-Driven Ocean Circulation. Part II: Time-Dependent Solutions, Journal of Physical Oceanography, 33(2003), 729-752 (with E. Simonnet, M. Ghil, K. Ide, and R. Temam).

[48] Low-Frequency Variability in Shallow Water Models of the Wind-Driven Ocean Circulation. Part I: Steady State Solutions, Journal of Physical Oceanography, 33(2003), 712-728 (with E. Simonnet, M. Ghil, K. Ide, and R. Temam).

[40] Smooth solutions and attractor dimension bounds for planetary geostrophic ocean models, Quarterly Journal of Royal Meteorological Society, 126:566(2000), 1977-1981 (with R. Samelson and R. Temam)

[37] On Mathematical Problems for the Primitive Equations of the Ocean: The Mesoscale Midlatitude Case, Nonlinear Analysis, 40(2000) , 439-482 (with J.-L. Lions and R. Temam)

[35] Mathematical Problems in Meteorology and Oceanography, Bull. Amer. Meteorol. Soc., 81:2(2000), 319-321 (with R. Temam)

[34] Remarks on the Planetary Geostrophic Model of Gyre Scale Ocean Circulation, Differential and Integral Equations, 13(2000), 1--14 (with R. Samelson and R. Temam)

[33] On a Wind-Driven, Double-Gyre, Quasi-Geostrophic Ocean Model: Numerical Simulations and Structural Analysis, Journal of Computational Physics, 155(1999), 387-409 (with J. Shen and T. Tachim Medjo)

[31] An Efficient Numerical Scheme for the Primitive Equations of the Atmosphere, SIAM J. Numer. Analysis, 36:3(1999), 719-737 (with Jie Shen)

[28] Some Mathematical Properties of the Planetary Geostrophic Equations for Large-Scale Ocean Circulation, Applicable Analysis, 70:1-2(1999), 147-173 (with R. Samelson and R. Temam)

[27] Successive bifurcations in a shallow-water ocean model, Dedicated to M. Holt on his 80th Birthday, in Sixteenth International Conference on Numerical Methods in Fluid Dynamics, Edited by Charles-Henri Bruneau, Lecture Notes in Physics, Vol 515, Springer-Verlag, pp. 225-230, 1998 (with E. Simonnet, R. Temam, M. Ghil and K. Ide)

[23] A Simple Model for the General Circulation of the Atmosphere, Dedicated Peter D. Lax and Louis Nirenberg on the Occasion of their 70th Birthdays, Comm. Pure Appl. Math., 50:8(1997), 707-752 (with J.-L. Lions and R. Temam)

[21] Physical Interpretations of the Attractor for a Simple Model of Atmospheric Circulation, Journal of Atmosphere Sciences, 54:9(1997), 1137-1143 (with J.-L. Lions, O. Manley and R. Temam)

[17] Mathematical Theory for the Coupled Atmosphere-Ocean Models, J. Math. Pures et Appl., 74:2 (1995), 105-163 (with Jacques-Louis Lions and Roger Temam)

[15] Geostrophic Asymptotics of the Primitive Equations of the Atmosphere, Topological Methods in Nonlinear Analysis, Special Issue Dedicated to Jean Leray, 4(1994), 253-287 (with J.-L. Lions and R. Temam)

[14] Probl\`emes \`a Fronti\`ere Libre pour les Mod\`eles
Coupl\'es de l'Oc\'ean et de l'Atmosph\`ere, C. R. Acad. Sci. Paris, S\'er. I, 318(1994), 1165-1171 (with Jacques-Louis Lions and Roger Temam)

[12] Numerical Analysis of Coupled Atmosphere-Ocean Models, in Computational Mechanics Advance, 1(1993), 55-120,
J.T. Oden ed., Elsevier (with Jacques-Louis Lions and Roger Temam)

[11] Models of the Coupled Atmosphere and Ocean,
in {\it Computational Mechanics Advance}, Vol. 1, 1993, 3-54, J.T. Oden ed., Elsevier (with Jacques-Louis Lions and Roger Temam)

[10] Mod\`eles et Analyse Math\'ematique du Syst\`eme
Oc\'ean/Atmosph\`ere, II. Couplage, C. R. Acad. Sci. Paris, S\'er. I,
316(1993), 211-215 (with Jacques-Louis Lions and Roger Temam)

[9] Mod\`eles et Analyse Math\'ematique du Syst\`eme Oc\'ean/Atmosph\`ere, I. Structure des sous Syst\`emes, C. R. Acad. Sci. Paris, S\'er. I, 316(1993), 113-119 (with Jacques-Louis Lions and Roger Temam)

[8] On the Equations of the Large-scale Ocean, Nonlinearity, 5(1992), 1007-1053 (with Jacques-Louis Lions and Roger Temam)
[7] New Formulations of the Primitive Equations of Atmosphere and Applications, Nonlinearity, 5(1992), 237-288 (with Jacques-Louis Lions and Roger Temam)

[3] On Stationary Solutions to the Equations of Large Scale Atmosphere, in Nonlinear Analysis, W. Chen ed., Lanzhou University Press, 1989

[2] Some Properties of Solutions for the Equations of Large Scale
Atmosphere: Nonlinear Adjustment to the Time Independent External Forcing, Sciences in China, 38(1989), 328-336 (with J. Chou and J. Huang)
[0] On Solvability of the Equations of Large-Scale Atmospheric
Equations, Ph D dissertation, 1988

Last updated on March 20, 2006