On upper bounds for infinite Prandtl number convection with or without rotation

Journal of Mathematical Physics

Volumn 42, Issue 2, 2001, Pages 784-795

  Doering, Charles R ^a   Constantin, Peter ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035529626     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1336157     Document Type: Article

References (25)

1. E. A. Spiegel, Annu. Rev. Astron. Astrophys. 9, 323 (1971).
2. See, for example: P. E. Van Keken, Earth Planet. Sci. Lett. 148, 1 (1997).
3. J. Pedlosky, Geophysical Fluid Dynamics (Springer, Berlin, 1979).
4. E. Siggia, Annu. Rev. Fluid Mech. 26, 137 (1997).
5. F. Heslot, B. Castaing, and A. Libchaber, Phys. Rev. A 36, 5870 (1987).
6. S. Cioni, S. Ciliberto, and J. Sommeria, J. Fluid Mech. 335, 111 (1997).
7. X. Chavanne, F. Chilla, B. Castaing, B. Hebral, B. Chabaud, and J. Chaussy, Phys. Rev. Lett. 79, 3648 (1997).
8. J. Glazier, T. Segawa, A. Naert, and M. Sano, Nature (London) 398, 307 (1999).
9. J. Niemela, L. Skrbek, K. R. Sreenivasan, and R. J. Donnelly, Nature 404, 837-840 (2000).
10. R. Kraichnan, "Turbulent Thermal Convection at Arbitrary Prandtl Number," Phys. Fluids 5, 1374 (1962).
11. C. Doering and P. Constantin, Phys. Rev. E 53, 5957 (1996).
12. L. N. Howard, J. Fluid Mech. 17, 405 (1963); for a review see: L. N. Howard, Annu. Rev. Fluid Mech. 4, 473 (1972).
13. L. N. Howard, J. Fluid Mech. 17, 405 (1963); for a review see: L. N. Howard, Annu. Rev. Fluid Mech. 4, 473 (1972).
14. W. V. R. Malkus, Proc. R. Soc. London, Ser. A 225, 196 (1954).
15. L. N. Howard, in Applied Mechanics, Proc. 11th Cong. Applied Mech., edited by H. Görtler (Springer-Verlag, Berlin, 1966), pp. 1109-1115.
16. S.-K. Chan, Stud. Appl. Math. 50, 13 (1971).
17. P. Constantin and C. R. Doering, J. Stat. Phys. 94, 159 (1999).
18. T. H. Rossby, J. Fluid Mech. 36, 309 (1969); Y. Liu and R. Ecke. Phys. Rev. Lett. 79, 2257 (1997).
19. T. H. Rossby, J. Fluid Mech. 36, 309 (1969); Y. Liu and R. Ecke. Phys. Rev. Lett. 79, 2257 (1997).
20. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961); P. Drazin and W. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
21. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, 1961); P. Drazin and W. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
22. R. A. Worthing, Phys. Lett. A 237, 381 (1998).
23. P. Constantin, C. Hallstrom, and V. Putkaradze, Physica D 125, 275 (1999).
24. P. Constantin, C. Hallstrom, and V. Putkaradze, J. Math. Phys. 42, 773 (2001).
25. P. Constantin, Contemp. Math. 238, 77 (1999).