The real butterfly effect

Nonlinearity

Volumn 27, Issue 9, 2014, Pages

  Palmer, T N ^a   Doring A ^a,b   Seregin, G ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

butterfly effect; chaos; finite time predictability; surface quasigeostrophic equations

Indexed keywords

EID: 84906700277     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/27/9/R123     Document Type: Review

References (31)

1. Blumen W 1978 Uniform potential vorticity flow: I. Theory of wave interactions and two-dimensional turbulence J. Atmos. Sci. 35 774-83
2. Bourgain J and Pavlovich N 2008 Ill-posedness of the Navier-Stokes equations in a critical space in 3D J. Funct. Anal. 255 2233-47
3. Cao C and Titi E S 2007 Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics Ann. Math. 166 245-67
4. Durran D R and Gingrich M 2014 Atmospheric predictability: why atmospheric butterflies are not of practical importance J. Atmos. Sci. 71 2476-8
5. Fefferman Ch L www.claymath.org/millennium/Navier-Stokes equations
6. Gleick J 1988 Chaos: Making of a New Science (London: Penguin) 352pp
7. Held I M, Pierrehumbert R T, Garner S T and Swanson K L 1995 Surface quasi-geostrophic dynamics J. Fluid Mech. 282 1-20 (Pubitemid 26463360)
8. Hohenegger C and Schär C 2007 Atmospheric predictability at synoptic versus cloud-resolving scales Bull. Am. Meteorol. Soc. 88 1783-93 (Pubitemid 350302553)
9. Hopf E 1950-51 Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen Math. Nachr. 4 213-31
10. Jia H and Sverak V Are the incompressible 3D Navier-Stokes equations locally ill-posed in the natural energy space? arXiv:1306.2136
11. Kiselev A A and Ladyenskaya O A 1957 On the existence and uniqueness of the solution of the nonstationary problem for a viscous, incompressible fluid (in Russian) Izv. Akad. Nauk SSSR. Ser. Mat. 21 655-80
12. Ladyzhenskaya O A 1958 Global solvability of a boundary value problem for the Navier-Stokes equations in the case of two spatial variables Dokl. USSR 123 427-9
13. Ladyzhenskaya O A 1970 Mathematical Problems of the Dynamics of Viscous Incompressible Fluids 2nd edn (Moscow: Nauka)
14. Lemarié-Riesset P G Recent Developments in the Navier-Stokes Problem (Research Notes in Mathematics Series vol 431) (Boca Raton, FL: CRC Press)
15. Leith C and Kraichnan R 1972 Predictability of turbulent flows J. Atmos. Sci. 29 1041-58
16. Leray J 1934 Sur le mouvement d'un liquide visqueux emplissant l'espace Acta Math. 63 193-248
17. Lilly D K 1973 Lectures in sub-synoptic scales of motions and two-dimensional turbulence Dynamic Meteorology ed P Morel (Boston, MA: Reidel) pp 353-418
18. Lorenz E N 1963 Deterministic nonperiod flow J. Atmos. Sci. 20 130-41
19. Lorenz E N 1969 The predictability of a flow which possesses many scales of motion Tellus 3 290-307
20. Lorenz E N 1993 The Essence of Chaos (Seattle: University of Washington Press) 227pp
21. Lovejoy S and Schertzer D 2013 The Weather and Climate: Emergent Laws and Multifractal Cascades (Cambridge: Cambridge University Press)
22. Majda A J and Bertozzi A L 2002 Vorticity, Incompressible Flow (Cambridge: Cambridge University Press)
23. Métais O and Lesieur M 1986 Statistical predictability of decaying turbulence J. Atmos. Sci. 43 857-70
24. Nastrom G D and Gage K S 1985 A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft J. Atmos. Sci. 42 950-60 (Pubitemid 15530025)
25. Palmer T N 2000 Predicting uncertainty in forecasts of weather and climate Rep. Prog. Phys. 63 71-116
26. Palmer T N 2001 A nonlocal dynamical perspective on model error: a proposal for nonlocal stochastic-dynamic parametrization in weather and climate prediction models Q. J. R. Meteorol. Soc. 127 279-304 (Pubitemid 32257521)
27. Palmer T N 2002 The Economic value of ensemble forecasts as a tool for risk assessment: from days to decades (The Royal Meteorlogical Society 2001 Symons Memorial Lecture) Q. J. R. Meteorol. Soc. 128 747-74 (Pubitemid 34495135)
28. Rodwell M et al 2013 Characteristics of occasional poor medium-range weather forecasts for Europe Bull. Am. Meteorol. Soc. 94 1393-405
29. Rotunno R and Snyder C 2008 A generalisation of Lorenz's model for the predictability of flows with many scales of motion J. Atmos. Sci. 65 1063-76 (Pubitemid 351638353)
30. Simmons A J and Hollingsworth A 2002 Some aspects of the improvement in skill of numerical weather prediction Q. J. Roy. Meteorol. Soc. 128 647-77 (Pubitemid 34246914)
31. Wiin-Nielsen A 1967 On the annual variation and spectral distribution of atmospheric energy Tellus 19 540-59