Lagrangian chaos: Transport, mixing and diffusion in fluids

La Rivista del Nuovo Cimento (1971-1977) - Tập 14 - Trang 1-80 - 2008
A. Crisanti1, M. Falcioni1, A. Vulpiani1, G. Paladin2
1Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, Italy
2Dipartimento di Fisica, Università dell’Aquila, Coppito-L’Aquila, Italy

Tài liệu tham khảo

[ATI89]S. Adachi, M. Toda andK. Ikeda:J. Phys. A,22, 3291 (1989). [A72]J. K. Aggarwal:Notes on Nonlinear Systems (Van Nostrand, 1972). [A84]H. Aref:J. Fluid Mech.,143, 1 (1984). [AB86]H. Aref andS. Balachandar:Phys. Fluids,29, 3515 (1986). [A63]V. I. Arnold:Russ. Math. Survey,18, 9 (1963). [A65]V. I. Arnold:C. R. Acad. Sci. Paris A,261, 17 (1965). [A76]V. I. Arnold:Methodes Mathematiques de la Mécanique Classique (Mir, Moscow, 1976). [AA68]V. I. Arnold andA. Avez:Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968). [A83]W. Arter:Phys. Lett. A,97, 171 (1983). [BBLS87]A. Babiano, C. Basdevant, B. Legras andR. Sadourny:J. Fluid Mech.,183, 379 (1987). [BBS84]A. Babiano, C. Basdevant andR. Sadourny:C. R. Acad. Sci. Paris,299, 495 (1984). [B52]G. K. Batchelor:Proc. R. Soc. A,213, 349 (1952). [B59]G. K. Batchelor:J. Fluid Mech.,5, 113 (1959). [B86]B. J. Bayly:Phys. Rev. Lett.,57, 2800 (1986). [BC87]B. J. Bayly andS. Childress:Phys. Rev. Lett.,59, 1573 (1987). [BG86]G. Benettin andG. Gallavotti:J. Stat. Phys.,44, 293 (1986). [BGGS80]G. Benettin, A. Giorgilli, L. Galgani andJ. M. Strelcyn:Mecanica,15, 9 and 21 (1980). [BS78]G. Benettin andJ. M. Strelcyn:Phys. Rev. A,17, 2157 (1978). [BPPV84]R. Benzi, G. Paladin, G. Parisi andA. Vulpiani:J. Phys. A,17, 3521 (1984). [BPPV85]R. Benzi, G. Paladin, G. Parisi andA. Vulpiani:J. Phys. A,18, 2157 (1985). [BR70]H. L. Berk andK. V. Roberts: inMethods in Computational Physics, Vol. 9, edited byB. Adler, S. Fernbach andM. Rotenberg (New York, Academic Press, 1970), p. 87. [B83]M. Berry: inChaotic Behaviour of Deterministic Systems, edited byG. Jooss, R. H. G. Helleman andR. Stora (North-Holland Publ. Comp., 1983). [BPTV88]D. Bessis, G. Paladin, G. Turchetti andS. Vaienti:J. Stat. Phys.,51, 109 (1988). [B27]G. D. Birkhoff:Dynamical Systems (AMS Publications, 1927). [BF79]C. Boldrighini andV. Franceschini:Commun. Math. Phys.,64, 159 (1979). [C22]T. Carleman:C. R. Acad. Sci. Paris,1174, 1680 (1922). [CCTT87]J. Chaiken, C. K. Chu, M. Tabor andQ. M. Tan:Phys. Fluids,30, 687 (1987). [C43]S. Chandrasekhar:Rev. Mod. Phys.,15, 1 (1943). [C70]S. Childress:J. Math. Phys.,11, 3063 (1970). [CS89]S. Childress andA. M. Soward:J. Fluid Mech.,205, 99 (1989). [C79]B. V. Chirikov:Phys. Rep.,52, 263 (1979). [C69]W. J. Cocke:Phys. Fluids,12, 2488 (1969). [C71]W. J. Cocke:Phys. Fluids,14, 1624 (1971). [C89]P. Collet:Workshop on Small Diffusivity Dynamos and Dynamical Systems (Nice, 1989). [C51]S. Corrsin:J. Appl. Phys.,22, 469 (1951). [C62]S. Corrsin: inMécanique de la Turbulence, edited byA. Favre (CNRS, Paris, 1962), p. 27. [CFPV90a]A. Crisanti, M. Falcioni, G. Paladin andA. Vulpiani:J. Phys. A: Math. Gen.,23, 3307 (1990). [CFPV90b]A. Crisanti, M. Falcioni, G. Paladin andA. Vulpiani:Physica A,166, 305 (1990). [CFPTV91]A. Crisanti, M. Falcioni, A. Provenzale, P. Tanga andA. Vulpiani:to appear (1991). [CFPrV90]A. Crisanti, M. Falcioni, A. Provenzale andA. Vulpiani:Phys. Lett. A,150, 79 (1990). [DFGHMS86]T. Dombre, U. Frisch, J. M. Greene, M. Hénon, A. Mehr andA. M. Soward:J. Fluid Mech.,167, 353 (1986). [DM90]I. T. Drummond andW. Münch:J. Fluid Mech.,215, 45 (1990). [DM91]I. T. Drummond andW. Münch:J. Fluid Mech.,225, 529 (1991). [ER85]J.-P. Eckmann andD. Ruelle:Rev. Mod. Phys.,57, 617 (1985). [FPV88]M. Falcioni, G. Paladin andA. Vulpiani:J. Phys. A: Math. Gen.,21, 3451 (1988). [FPV89]M. Falcioni, G. Paladin andA. Vulpiani:Europhys. Lett.,10, 201 (1989). [FV89]M. Falcioni andA. Vulpiani:J. Phys. A: Math. Gen.,22, 1201 (1989). [FKP88]M. Feingold, L. P. Kadanoff andO. Piro:J. Stat. Phys.,50, 529 (1988). [F71]W. Feller:An Introduction to Probability Theory and its Applications (New York, John Wiley and Sons, 1971). [FO88]J. M. Finn andE. Ott:Phys. Rev. Lett.,60, 760 (1988). [FO90]J. M. Finn andE. Ott:Phys. Fluids B,2, 916 (1990). [GF84]D. J. Galloway andU. Frisch:Geophys. Astrophys. Fluid Dyn.,29, 13 (1984). [GF87]D. J. Galloway andU. Frisch:J. Fluid Mech.,180, 557 (1987). [G83]P. Grassberger:Phys. Lett. A,97, 227 (1983). [GP83]P. Grassberger andI. Procaccia:Phys. Rev. A,28, 2591 (1983). [GH83]J. Guckenheimer andP. Holmes:Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer Verlag, 1983). [G90]M. C. Gutzwiller:Chaos in Classical and Quantum Mechanics (Springer Verlag, 1990). [HJKPS86]T. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia andB. I. Shraiman Phys. Rev. A,33, 1141 (1986). [H19]F. Hausdorff:Math. Ann.,79, 157 (1919). [H66]M. Hénon:C. R. Acad. Sci. Paris A,262, 312 (1966). [HH64]M. Hénon andC. Heiles:Astron. J.,69, 73 (1964). [HP83]H. G. E. Hentschel andI. Procaccia:Phisica D,8, 435 (1983). [H59]J. O. Hinze:Turbulence (New York, McGraw-Hill, 1959). [H90]P. Holmes:Phys. Rep.,193, 137 (1990). [HHIM90]T. Horita, H. Hata, R. Ishizaki andH. Mori:Prog. Theor. Phys.,83, 1065 (1990). [IKTTY89]M. B. Isichenko, Ya. L. Kalda, E. B. Tatarinova, O. V. Tel’kovskaya andV. V. Yan’kov:Soc. Phys. JETP,69, 517 (1989). [I90]F. M. Izrailev:Phys. Rep.,196, 299 (1990). [KST90]P. A. Kalugin, A. V. Sokol andE. B. Tatarinova:Europhys. Lett.,13, 417 (1990). [K57]A. I. Khinchin:Mathematical Foundation of Information Theory (Dover Publ., New York, 1957). [KD84]R. G. Kleva andJ. F. Drake:Phys. Fluids,27, 1686 (1984). [K54]A. N. Kolmogorov:Dokl. Akad. Nauk SSSR,98, 527 (1954). [K74]R. A. Kraichnan:J. Fluid Mech.,64, 737 (1974). [K84]J. A. Krommes: inHandbook of Plasma Physics, Vol. 2, edited byM. N. Rosenbluth andR. Z. Sagdeev (Elsevier Science Publishers, 1984). [KRS83]L. M. Kuznetsova, M. I. Rabinovich andM. M. Sushchik:Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana,19, 36 (1983). [L45]H. Lamb:Hydrodynamics (New York, Dover Publ., 1945). [LL87]L. D. Landau andL. Lifshitz:Fluid Mechanics (New York, Pergamon Press, 1987). [L87]J. Lee:Physica D,24, 54 (1987). [LH85]M. Lesieur andJ. Herring:J. Fluid Mech.,161, 77 (1985). [L73]D. C. Leslie:Developments in the Theory of Turbulence (Oxford, Clarendon Press, 1973). [LL83]A. J. Lichtenberg andM. A. Liebermann:Regular and Stochastic Motions (Berlin, Springer Verlag, 1983). [L63]E. N. Lorenz:J. Atm. Sci.,20, 130 (1963). [L62]J. L. Lumley: inMécanique de la Turbulence, edited byA. Favre (CNRS, Paris, 1962), p. 17. [LS89]R. Lupini andS. Siboni:Nuovo Cimento B,103, 237 (1989). [MPV86]A. Malagoli, G. Paladin andA. Vulpiani:Phys. Rev. A,34, 1550 (1986). [M75]B. B. Mandelbrot:J. Fluid Mech.,72, 401 (1975). [M82]B. B. Mandelbrot:The Fractal Geometry of Nature (New York, Freeman, 1982). [MM75]J. E. Marsden andM. McCracken:The Hopf Bifurcation and its Applications (Cambridge, Mass., MIT Press, 1975). [M90]J. C. Maxwell:The Scientific Papers, Vol 2 (Cambridge UK, Cambridge University Press, 1890). [MO87]R. McWilliams andM. Okubo:Phys. Fluids,30, 2840 (1987). [M63]V. K. Melnikov:Trans. Moscow Math. Soc.,12, 1 (1963). [M83]H. K. Moffat:Rep. Prog. Phys.,46, 621 (1983). [MRS84]S. A. Molchanov, A. A. Ruzmaikin andD. D. Sokoloff:Geophys. Astrophys. Fluid Dyn.,30, 241 (1984). [MY75]A. S. Monin andA. M. Yaglom:Statistical Fluid Mechanics, Vol. 2 (Cambridge, Mass., MIT Press, 1975). [MS84]E. W. Montroll andM. F. Schlesinger: inStudies in Statistical Mechanics, Vol. 11, edited byA. W. Montroll andJ. Lebowitz (Amsterdam, North-Holland, 1984). [M62]J. Moser:Nachr. Akad. Wiss. Göttingen Math-Phys KC 2,1, 15 (1962). [N77]N. N. Nekhoroshev:Russ. Math. Survey,32, 1 (1977). [O49]A. M. Obukhov:Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz.,13, 58 (1949). [O70]S. A. Orszag:Phys. Fluids,13, 2211 (1970). [OC91]Osborne andR. Caponio:Phys. Rev. Lett.,64, 1733 (1991). [OKPB86]A. R. Osborne, A. D. Kirwan, A. Provenzale andL. Bergamasco:Physica D,23, 75 (1986). [O68]V. I. Oseledec:Trans. Moscow Math. Soc.,19, 197 (1968). [OA88]E. Ott andT. M. jr.Antonsen:Phys. Rev. Lett.,61, 2839 (1988). [OA89]E. Ott andT. M. jr.Antonsen:Phys. Rev. A,39, 3660 (1989). [OA90]E. Ott andT. M. jr.Antonsen:Phys. Rev. Lett.,64, 699 (1990). [OP91]M. Ottaviani andM. Pettini:Int. J. Mod. Phys. B,5, 1243 (1991). [O89]J. M. Ottino:The Kinematic of Mixing: Stretching, Chaos and Transport (Cambridge Univ. Press, 1989). [O90]J. M. Ottino:Ann. Rev. Fluid Mech.,22, 207 (1990). [OLRS88]J. M. Ottino, C. W. Leong, H. Rising andP. D. Swanson:Nature,333, 419 (1988). [PV87a]G. Paladin andA. Vulpiani:Phys. Rep.,156, 147 (1987). [PV87b]G. Paladin andA. Vulpiani:Phys. Rev. A,35, 1971 (1987). [PF85]G. Parisi andU. Frisch: inTurbulence and Predictability of Geophysical Flows and Climatic Dynamics, edited byN. Ghil, R. Benzi andG. Parisi (North-Holland, 1985), p. 84. [P88]R. A. Pasmanter:Fluid Dyn. Res.,3, 320 (1988). [PV84]M. Pettini andA. Vulpiani:Phys. Lett. A,106, 207 (1984). [PVMDOB88]M. Pettini, A. Vulpiani, J. H. Misguich, M. De Leener, J. Orban andR. Balescu:Phys. Rev. A,38, 344 (1988). [P99]H. Poincaré:Les Methodes Nouvelles de la Mécanique Celeste, Vol. 1–3 (Gautier Villars, Paris, 1899). [P85]Y. Pomeau:C. R. Acad. Sci. Paris,301, 1323 (1985). [P84]I. Procaccia:J. Stat. Phys.,36, 649 (1984). [R22]L. F. Richardson:Weather Prediction by Numerical Process (Cambridge Univ. Press, 1922). [RS78]H. A. Rose andP. L. Sulem:J. Phys. (Paris),39, 441 (1978). [RBDH87]M. N. Rosenbluth, A. L. Berk, I. Doxas andW. Horton:Phys. Fluids,30, 2636 (1987). [S87]B. I. Shraiman:Phys. Rev. A,36, 261 (1987). [SG88a]T. H. Solomon andJ. P. Gollub:Phys. Rev. A,38, 6280 (1988). [SG88b]T. H. Solomon andJ. P. Gollub:Phys. Fluids,31, 1372 (1988). [S83]Y. S. Sun:Celest. Mech.,30, 7 (1983). [S84]Y. S. Sun:Celest. Mech.,33, 111 (1984). [T89]T. Tajima:Computational Plasma Physics (Addison-Wesley Publ. Comp. Inc., 1989). [T53]G. I. Taylor:Proc. R. Soc. A,219, 186 (1953). [T54]G. I. Taylor:Proc. R. Soc. A,225, 473 (1954). [TFR84]TFR Group:Plasma Phys. Contr. Fusion,26, 1045 (1984). [T88]D. J. Tritton:Physical Fluid Dynamics (Oxford Science Publications, 1988). [V89]A. Vulpiani:Physica D,38, 372 (1989). [WBS90]L. P. Wang, T. D. Burton andD. E. Stock:Phys. Fluids A,2, 1305 (1990). [WBS91]L. P. Wang, T. D. Burton andD. E. Stock:Phys. Fluids A,3, 1073 (1991). [W85]N. O. Weiss: inSolar System Magnetic Fields, edited byE. R. Priest (D. Reidel P. C., 1985), p. 156. [WK89]J. B. Weiss andE. Knoblock:Phys. Rev. A,40, 2579 (1989). [W88]S. Wiggins:Global Bifurcations and Chaos: Analytical Methods (Springer Verlag, 1988). [YGO90]L. Yu, C. Grebogi andE. Ott: inNonlinear Structures in Physical Systems, edited byL. Lam andH. C. Morris (Springer Verlag, 1900). p. 223. [Z81]G. M. Zaslavsky:Phys. Rep.,80, 157 (1981). [Z57]Ya. B. Zel’dovich:Sov. Phys. JETP,4, 460 (1957). [ZMRS84]Ya. B. Zel’dovich, S. A. Molchanov, A. A. Ruzmaikin andD. D. Sokoloff:J. Fluid Mech.,144, 1 (1984). [ZR86]Ya. B. Zel’dovich andA. A. Ruzmaikin: inNonlinear Phenomena in Plasma Physics and Hydrodynamics, edited byR. Z. Sagdeev (Moscow, M.I.R. Publ., 1986), p. 119.