Statistics of an unstable barotropic jet from a cumulant expansion

Journal of the Atmospheric Sciences

Volumn 65, Issue 6, 2008, Pages 1955-1966

  Marston, J Brad ^a   Conover, E ^a   Schneider, Tapio ^b  

^a BROWN UNIVERSITY   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DIRECT NUMERICAL SIMULATION; RELAXATION PROCESSES; SPHERES; STATISTICAL METHODS; STATISTICS;

AMERICAN METEOROLOGICAL SOCIETY (AMS); BARO-TROPIC FLOWS; BAROTROPIC JET; CUMULANT; LINEAR RELAXATIONS; NUMERICAL SIMULATIONS; ROTATING SPHERES; SECOND ORDERS;

RELAXATION TIME;

BAROTROPIC MOTION; CRITICAL FLOW; JET FLOW; NUMERICAL MODEL; STATISTICAL ANALYSIS; TURBULENT FLOW;

EID: 45849137876     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/2007JAS2510.1     Document Type: Article

References (32)

1. Arakawa, A., 1966: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I. J. Comput. Phys., 1, 119-143.
2. Cho, J. Y.-K., and L. M. Polvani, 1996: The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids, 8, 1531-1552.
3. Frisch, U., 1995: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, 296 pp.
4. Gates, W. L., and C. A. Riegel, 1962: A study of numerical errors in the integration of barotropic flow on a spherical grid. J. Geophys. Res., 67, 773-784.
5. Held, I. M., 1978: The vertical scale of an unstable baroclinic wave and its importance for eddy heat flux parameterizations. J. Atmos. Sci., 35, 572-576.
6. Herring, J. R., 1963: Investigation of problems in thermal convection. J. Atmos. Sci., 20, 325-338.
7. Holloway, G., 1986: Estimation of oceanic eddy transports from satellite altimetry. Nature, 323, 243-244.
8. Holloway, G., and M. C. Hendershott, 1977: Stochastic closure for nonlinear Rossby waves. J. Fluid Mech., 82, 747-765.
9. Holloway, G., and S. S. Kristmannsson, 1984: Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech., 141, 27-50.
10. Huang, H,-P., B. Galperin, and S. Sukoriansky, 2001: Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere. Phys. Fluids, 13, 225-240.
11. Legras, B., 1980: Turbulent phase shift of Rossby waves. Geophys. Astrophys. Fluid Dyn., 15, 253-281.
12. Lindzen, R. S., A. J. Rosenthal, and R. Farrell. 1983: Charney's problem for baroclinic instability applied to barotropic instability. J. Atmos. Sci., 40, 1029-1034.
13. Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere. WMO Publications, Vol. 218, World Meteorological Organization, 161 pp.
14. Ma, O., and J. B. Marston, 2005: Exact equal time statistics of Orszag-McLaughlin dynamics investigated using the Hopf characteristic functional approach. J. Stat. Mech., 2005, P10007, doi:10.1088/1742-5468/2005/10/P10007.
15. Majda, A. J., and X. Wang, 2006: Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows. Cambridge University Press, 564 pp.
16. Maslowe, S. A., 1986: Critical layers in shear flows. Anna. Rev. Fluid Mech., 18, 405-432.
17. McComb, W. D., 2004: Renormalization Methods: A Guide for Beginners. Oxford University Press, 330 pp,
18. Miller, J., 1990: Statistical mechanics of Euler equations in two dimensions. Phys. Rev. Lett., 65, 2137-2140.
19. Nielsen, J. E., and M. R. Schoeberl, 1984: A numerical simulation of barotropic instability. Part II: Wave-wave interaction. J. Atmos. Sci., 41, 2869-2881.
20. O'Gorman, P. A., and T. Schneider, 2007: Recovery of atmospheric flow statistics in a general circulation model without nonlinear eddy-eddy interactions. Geophys. Res. Lett., 34, L22801, doi: 10.1029/2007GL031779.
21. Orszag, S. A., 1977: Statistical theory of turbulence. Fluid Dynamics 1973, Les Houches Summer School of Theoretical Physics, R. Balian and J. L. Peube, Eds., Gordon and Breach, 235-374.
22. Robert, R., and J. Sommeria, 1991: Statistical equilibrium states for two-dimensional flows. J. Fluid Mech., 229, 291-310.
23. Salmon, R., 1998: Lecatres on Geophysical Fluid Dynamics. Oxford University Press, 378 pp.
24. Schneider, T., and C. C. Walker, 2006: Self-organization of atmospheric macroturbulence into critical states of weak nonlinear eddy-eddy interactions. J. Atmos. Sci., 63, 1569-1586.
25. Schoeberl, M. R., and R. S. Lindzen, 1984: A numerical simulation of barotropic instability. Part I: Wave-mean flow interaction. J. Atmos. Sci., 41, 1368-1379.
26. Schoeberl, M. R., and J. E. Nielsen, 1986: A numerical simulation of barotropic instability. Part III: Wave-wave interaction in the presence of dissipation. J. Atmos. Sci., 43, 1045-1050.
27. Shepherd, T. G., 1987: Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere. J. Fluid Mech., 184, 289-302.
28. Shepherd, T. G., 1988: Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows. J. Fluid Mech., 196, 291-322.
29. Stammer, D., 1998: On eddy characteristics, eddy transports, and mean flow properties. J. Phys. Oceanogr., 28, 727-739.
30. Stewartson, K., 1981: Marginally stable inviscid flows with critical layers. IMA J. Appl. Math., 27, 133-175.
31. Turkington, B., A. Majda, K. Haven, and M. DiBattista, 2001: Statistical equilibrium predictions of jets and spots on Jupiter. Proc. Natl. Acad. Sci. USA, 98, 12 346-12 350.
32. Weichman, P. B., 2006: Equilibrium theory of coherent vortex and zonal jet formation in a system of nonlinear Rossby waves. Phys. Rev. E, 73, 036 313, doi:10.1103/PhysRevE.73.036313.