Dissipative Quasi-geostrophic Dynamics under Random Forcing

Journal of Mathematical Analysis and Applications

Volumn 228, Issue 1, 1998, Pages 221-233

  Brannan, James R ^a   Duan, Jinqiao ^a   Wanner, Thomas ^b  

^a CLEMSON UNIVERSITY   (United States)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Dissipation; Quasi geostrophic model; Random forcing; Stochastic partial differential equation

Indexed keywords

EID: 0001015361     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6128     Document Type: Article

References (23)

1. Adams R. Sobolev Spaces. 1975;Academic Press, New York.
2. Babin A., Mahalov A., Nicolaenko B. Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids. 15:1996;291-300.
3. Bennett A. F., Kloeden P. E. The dissipative quasigeostrophic equations. Mathematika. 28:1981;265-285.
4. Bourgeois A. J., Beale J. T. Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean. SIAM J. Math. Anal. 25:1994;1023-1068.
5. Cessi P., Ierley G. R. Symmetry-breaking multiple equilibria in quasigeostrophic, wind-driven flows. J. Phys. Oceanogr. 25:1995;1196-1205.
6. Cushman-Roisin B. Introduction to Geophysical Fluid Dynamics. 1994;Prentice Hall, Englewood Cliffs.
7. Da Prato G., Zabczyk J. Stochastic Equations in Infinite Dimensions. 1992;Cambridge Univ. Press, Cambridge.
8. Da Prato G., Zabczyk J. Ergodicity for Infinite Dimensional Systems. 1996;Cambridge Univ. Press, Cambridge.
9. Da Prato G., Debussche A., Temam R. Stochastic Burgers equation. NoDEA Nonlinear Differential Equations Appl. 1994;389-402.
10. DelSole T., Farrell B. F. A stochastically excited linear system as a model for quasigeostrophic turbulence: Analytic results for one- and two-layer fluids. J. Atmospheric Sci. 52:1995;2531-2547.
11. Embid P. F., Majda A. J. Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Comm. Partial Differential Equations. 21:1996;619-658.
12. Gilbarg D., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1983;Springer-Verlag, Berlin/New York.
13. Griffa A., Castellari S. Nonlinear general circulation of an ocean model driven by wind with a stochastic component. J. Marine Res. 49:1991;53-73.
14. Henry D. Geometric Theory of Semilinear Parabolic Equations. 1981;Springer-Verlag, Berlin.
15. Holloway G. Ocean circulation: Flow in probability under statistical dynamical forcing. Molchanov S., Woyczynski W. Stochastic Models in Geosystems. 1996;Springer-Verlag, Berlin/New York.
16. Klyatskin V., Gurarie D. Random topography in geophysical models. Molchanov S., Woyczynski W. Stochastic Models in Geosystems. 1996;Springer-Verlag, Berlin/New York.
17. Holm D. D. Hamiltonian formulation of the baroclinic quasigeostrophic fluid equations. Phys. Fluids. 29:1986;7-8.
18. Müller P. Stochastic forcing of quasi-geostrophic eddies. Adler R. J., Müller P., Rozovskii B. Stochastic Modelling in Physical Oceanography. 1996;Birkhäuser, Basel.
19. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. 1983;Springer-Verlag, Berlin/New York.
20. Pedlosky J. Geophysical Fluid Dynamics. 1987;Springer-Verlag, Berlin/New York.
21. Samelson R. M. Stochastically forced current fluctuations in vertical shear and over topography. J. Geophys. Res. 94:1989;8207-8215.
22. Schochet S. H. Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation. J. Differential Equations. 68:1987;400-428.
23. Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. 1988;Springer-Verlag, New York.