{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T08:54:57Z","timestamp":1742979297147,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":90,"publisher":"Springer New York","isbn-type":[{"type":"print","value":"9780387758886"},{"type":"electronic","value":"9780387304403"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-0-387-30440-3_215","type":"book-chapter","created":{"date-parts":[[2009,6,17]],"date-time":"2009-06-17T16:54:06Z","timestamp":1245257646000},"page":"3641-3661","source":"Crossref","is-referenced-by-count":0,"title":["Fluid Dynamics, Turbulence"],"prefix":"10.1007","author":[{"given":"Rudolf","family":"Friedrich","sequence":"first","affiliation":[]},{"given":"Joachim","family":"Peinke","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"215_CR1_215","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1017\/S0022112084000513","volume":"140","author":"F Anselmet","year":"1984","unstructured":"Anselmet F, Gagne Y, Hopfinger EJ, Antonia RA (1984) High order structurefunctions in turbulent shear flows. J\u00a0Fluid Mech 140:63","journal-title":"J Fluid Mech"},{"key":"215_CR2_215","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1209\/epl\/i1997-00116-1","volume":"37","author":"RA Antonia","year":"1997","unstructured":"Antonia RA, Ould-Rouis M, Zhu Y, Anselmet F (1997) Fourth\u2010order moments oflongitudinal- and transverse\u2010velocity structure functions. Europhys Lett 37:85","journal-title":"Europhys Lett"},{"key":"215_CR3_215","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1146\/annurev.fl.15.010183.002021","volume":"15","author":"H Aref","year":"1983","unstructured":"Aref H (1983) Integrable, chaotic, and turbulent vortex motion intwo\u2010dimensional flows. Ann Rev Fluid Mech 15:345","journal-title":"Ann Rev Fluid Mech"},{"key":"215_CR4_215","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.fluiddyn.2006.04.004","volume":"39","author":"H Aref","year":"2007","unstructured":"Aref H (2007) Vortices and polynomials. Fluid Dyn Res39:5","journal-title":"Fluid Dyn Res"},{"key":"215_CR5_215","volume-title":"Topological methods in hydrodynamics","author":"VI Arnold","year":"1999","unstructured":"Arnold VI, Khesin BA (1999) Topological methods in hydrodynamics. Springer,Berlin"},{"key":"215_CR6_215","doi-asserted-by":"crossref","unstructured":"Aronson D, L\u00f6fdahl LL (1993) The plane wake of a\u00a0cylinder. Measurements andinferences on the turbulence modelling. Phys Fluids A 5:1433","DOI":"10.1063\/1.858579"},{"key":"215_CR7_215","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1209\/0295-5075\/24\/4\/007","volume":"24","author":"R Benzi","year":"1993","unstructured":"Benzi R, Ciliberto S, Baudet C, Chavarria GR, Tripiccione R (1993) Extendedself\u2010similarity in the dissipation range of fully\u2010developed turbulence. Europhys Lett 24:275","journal-title":"Europhys Lett"},{"key":"215_CR8_215","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0167-2789(90)90035-N","volume":"46","author":"B Castaing","year":"1990","unstructured":"Castaing B, Gagne Y, Hopfinger EJ (1990) Velocity probability density functionsof high Reynolds number turbulence. Phys D 46:177","journal-title":"Phys D"},{"key":"215_CR9_215","unstructured":"Data provided by Chabaud B, Chanal O, CNRS Gernoble,France"},{"key":"215_CR10_215","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.physd.2006.04.011","volume":"218","author":"L Chevillard","year":"2006","unstructured":"Chevillard L, Roux SG, Leveque E, Mordant N, Pinton J-F, Arneodo A (2006) PhysD 218:77","journal-title":"Phys D"},{"key":"215_CR11_215","volume-title":"A mathematical introduction to fluid mechanics","author":"AJ Chorin","year":"2000","unstructured":"Chorin AJ, Marsden GE (2000) A\u00a0mathematical introduction to fluidmechanics. Springer, Berlin"},{"key":"215_CR12_215","doi-asserted-by":"crossref","first-page":"194502","DOI":"10.1103\/PhysRevLett.91.194502","volume":"91","author":"Y Cuypers","year":"2003","unstructured":"Cuypers Y, Maurel A, Petitjeans P (2003) Vortex burst as a\u00a0source ofturbulence. Phys Rev Lett 91:194502","journal-title":"Phys Rev Lett"},{"key":"215_CR13_215","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198568438.001.0001","volume-title":"Worlds of Flow","author":"O Darrigol","year":"2005","unstructured":"Darrigol O (2005) Worlds of Flow. Oxford University Press, Oxford"},{"key":"215_CR14_215","volume-title":"Turbulence","author":"PA Davidson","year":"2004","unstructured":"Davidson PA (2004) Turbulence. Oxford University Press, Oxford"},{"key":"215_CR15_215","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1103\/PhysRevLett.82.1680","volume":"82","author":"J Davoudi","year":"1999","unstructured":"Davoudi J, Tabar MRR (1999) Theoretical Model for Kramers\u2010Moyal'sdescription of Turbulence Cascade. Phys Rev Lett 82:1680","journal-title":"Phys Rev Lett"},{"key":"215_CR16_215","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511608803","volume-title":"Applied Analysis of the Navier\u2010Stokes Equations","author":"CR Doering","year":"1995","unstructured":"Doering CR, Gibbon JD (1995) Applied Analysis of the Navier\u2010StokesEquations. Cambridge University Press, Cambridge"},{"key":"215_CR17_215","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.physleta.2005.11.019","volume":"351","author":"S Eule","year":"2005","unstructured":"Eule S, Friedrich R (2005) A\u00a0note on a\u00a0random driven Burgersequation. Phys Lett A 351:238","journal-title":"Phys Lett A"},{"key":"215_CR18_215","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1103\/RevModPhys.78.87","volume":"78","author":"GL Eyink","year":"2006","unstructured":"Eyink GL, Sreenivasan KR (2006) Onsager and the theory of hydrodynamicturbulence. Rev Mod Phys 78:87","journal-title":"Rev Mod Phys"},{"key":"215_CR19_215","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1103\/RevModPhys.73.913","volume":"73","author":"G Falkovich","year":"2001","unstructured":"Falkovich G, Gawedzki K, Vergassola M (2001) Particles and fields in fluidturbulence. Rev Mod Phys 73:797","journal-title":"Rev Mod Phys"},{"key":"215_CR20_215","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546754","volume-title":"Navier\u2013Stokes Equation and Turbulence","author":"C Foias","year":"2001","unstructured":"Foias C, Rosa R, Manley O, Temam R (2001) Navier\u2013Stokes Equation andTurbulence. Cambridge University Press, Cambridge"},{"key":"215_CR21_215","doi-asserted-by":"crossref","first-page":"084501","DOI":"10.1103\/PhysRevLett.90.084501","volume":"90","author":"R Friedrich","year":"2003","unstructured":"Friedrich R (2003) Statistics of Lagrangian velocities in turbulentflows. Phys Rev Lett 90:084501","journal-title":"Phys Rev Lett"},{"key":"215_CR22_215","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1103\/PhysRevLett.78.863","volume":"78","author":"R Friedrich","year":"1997","unstructured":"Friedrich R, Peinke J (1997) Description of a\u00a0turbulent cascade bya\u00a0Fokker\u2013Planck equation. Phys Rev Lett 78:863","journal-title":"Phys Rev Lett"},{"key":"215_CR23_215","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0167-2789(96)00235-7","volume":"102","author":"R Friedrich","year":"1997","unstructured":"Friedrich R, Peinke J (1997) Statistical properties of a\u00a0turbulentcascade. Phys D 102:147","journal-title":"Phys D"},{"key":"215_CR24_215","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1209\/epl\/i1998-00124-7","volume":"41","author":"R Friedrich","year":"1998","unstructured":"Friedrich R, Zeller J, Peinke J (1998) A\u00a0Note in Three Point Statisticsof Velocity Increments in Turbulence. Europhys Lett 41:153","journal-title":"Europhys Lett"},{"key":"215_CR25_215","volume-title":"Importance of Fluctuations: Complexity in the View of Stochastic Processes within this issue","author":"R Friedrich","year":"2008","unstructured":"Friedrich R, Peinke J, Tabar MRR (2008) Importance of Fluctuations: Complexityin the View of Stochastic Processes within this issue. Springer, Berlin"},{"key":"215_CR26_215","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139170666","volume-title":"Turbulence. The legacy of Kolmogorov","author":"U Frisch","year":"1995","unstructured":"Frisch U (1995)Turbulence. The legacy of Kolmogorov. Cambridge University Press, Cambridge"},{"key":"215_CR27_215","volume-title":"Fundamental problematic issues in turbulence","author":"AV Fursikov","year":"1999","unstructured":"Fursikov AV (1999) The closure problem of the Friedmann\u2013Keller infinitechain of moment equations, corresponding to the Navier\u2013Stokes system. In: Gyr A, Kinzelbach W, Tsinober A (eds) Fundamental problematic issues inturbulence. Birkh\u00e4user, Basel"},{"key":"215_CR28_215","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1088\/0951-7715\/10\/6\/013","volume":"10","author":"B Galanti","year":"1997","unstructured":"Galanti B, Gibbon JD, Heritage M (1997) Vorticity alignment results for thethree\u2010dimensional Euler and Navier\u2013Stokes equations. Nonlinearity 10:1675","journal-title":"Nonlinearity"},{"key":"215_CR29_215","doi-asserted-by":"crossref","first-page":"2831","DOI":"10.1063\/1.858746","volume":"A5","author":"AD Gilbert","year":"1993","unstructured":"Gilbert AD (1993) A\u00a0cascade interpretation of Lundgrens stretched spiralvortex model for turbulent fine structure. Phys Fluids A5:2831","journal-title":"Phys Fluids"},{"key":"215_CR30_215","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1016\/j.physd.2007.11.006","volume":"237","author":"T Grafke","year":"2008","unstructured":"Grafke T, Homann H, Dreher J, Grauer R (2008) Numerical simulations of possiblefinite time singularities in the incompressible Euler equations: comparison of numerical methods. Phys D 237:1932","journal-title":"Phys D"},{"key":"215_CR31_215","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0378-4371(00)00223-5","volume":"286","author":"V Grassi","year":"2000","unstructured":"Grassi V, Leo R a, Soliani G, Tempesta P (2000) Vortices and invariantsurfaces generated by symmetries for the 3D Navier\u2013Stokes equations. Physica A 286:79","journal-title":"Physica A"},{"key":"215_CR32_215","doi-asserted-by":"crossref","first-page":"4850","DOI":"10.1103\/PhysRevLett.84.4850","volume":"84","author":"R Grauer","year":"1998","unstructured":"Grauer R, Marliani C, Germaschewski K (1998) Adaptive mesh refinement forsingular solutions of the incompressible Euler equations. Phys Rev Lett 84:4850","journal-title":"Phys Rev Lett"},{"key":"215_CR33_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8689-5","volume-title":"Fundamental problematic issues in turbulence","author":"A Gyr","year":"1999","unstructured":"Gyr A, Kinzelbach W, Tsinober A (1999) Fundamental problematic issues inturbulence. Birkh\u00e4user, Basel"},{"key":"215_CR34_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-88338-5","volume-title":"Synergetics, An Introduction","author":"H Haken","year":"1983","unstructured":"Haken H (1983) Synergetics, An Introduction. Springer,Berlin"},{"key":"215_CR35_215","volume-title":"Advanced Synergetics","author":"H Haken","year":"1987","unstructured":"Haken H (1987) Advanced Synergetics. Springer,Berlin"},{"key":"215_CR36_215","doi-asserted-by":"crossref","first-page":"026303","DOI":"10.1103\/PhysRevE.77.026303","volume":"77","author":"PE Hamlington","year":"2008","unstructured":"Hamlington PE, Schumacher J, Dahm WJA (2008) Local and nonlocal strain ratefields and vorticity alignment in turbulent flows. Phys Rev E 77:026303","journal-title":"Phys Rev E"},{"key":"215_CR37_215","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1103\/PhysRevLett.79.1257","volume":"79","author":"N Hatakeyama","year":"1997","unstructured":"Hatakeyama N, Kambe T (1997) Statistical laws of random strained vortices inturbulence. Phys Rev Lett 79:1257","journal-title":"Phys Rev Lett"},{"key":"215_CR38_215","first-page":"87","volume":"1","author":"E Hopf","year":"1957","unstructured":"Hopf E (1957) Statistical hydromechanics and functional calculus. J\u00a0Rat MechAnal 1:87","journal-title":"J Rat Mech Anal"},{"key":"215_CR39_215","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1017\/S0022112093002393","volume":"255","author":"J Jimenez","year":"1993","unstructured":"Jimenez J, Wray AA, Saffman PG, Rogallo RS (1993) The structure of intensevorticity in isotropic turbulence. J\u00a0Fluid Mech 255:65","journal-title":"J Fluid Mech"},{"key":"215_CR40_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-10411-8","volume-title":"The statistical dynamics of turbulence","author":"J Jovanovic","year":"2004","unstructured":"Jovanovic J (2004) The statistical dynamics of turbulence. Springer,Berlin"},{"key":"215_CR41_215","volume-title":"Vorlesungen \u00fcber mathematische Physik","author":"G Kirchhoff","year":"1883","unstructured":"Kirchhoff G (1883) Vorlesungen \u00fcber mathematische Physik, vol\u00a01, 3rdedn. Teubner, Leipzig","edition":"3"},{"key":"215_CR42_215","first-page":"19","volume":"32","author":"AN Kolmogorov","year":"1941","unstructured":"Kolmogorov AN (1941) Dissipation of energy in locally isotropicturbulence. Dokl Akad Nauk SSSR 32:19","journal-title":"Dokl Akad Nauk SSSR"},{"key":"215_CR43_215","first-page":"301","volume":"30","author":"AN Kolmogorov","year":"1941","unstructured":"Kolmogorov AN (1941) The local structure of turbulence in incompressibleviscous fluid for very large Reynold's numbers. Dokl Akad Nauk SSSR 30:301","journal-title":"Dokl Akad Nauk SSSR"},{"key":"215_CR44_215","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1017\/S0022112062000518","volume":"13","author":"AN Kolmogorov","year":"1962","unstructured":"Kolmogorov AN (1962) A\u00a0refinement of previous hypotheses concerning thelocal structure of turbulence in a\u00a0viscous incompressible fluid at high Reynolds number. J\u00a0Fluid Mech 13:82","journal-title":"J Fluid Mech"},{"key":"215_CR45_215","unstructured":"L'vov V, Procaccia I Hydrodynamic Turbulence: a\u00a019th Century Problem with a\u00a0Challenge for the 21st Centurs. arXiv:chao-dyn 96006015"},{"key":"215_CR46_215","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1063\/1.870397","volume":"12","author":"A La Porta","year":"2000","unstructured":"La Porta A, Voth G, Crawford AM, Alexander J, Bodenschatz E (2000) Fluidparticle acceleration in fully developped turbulence. Nature 409:1017; La Porta A, Voth G, Moisy F, Bodenschatz E (2001) Using cavitation to measurestatistics of low\u2010pressure events in large Reynolds\u2010number turbulence. Phys Fluids 12:1485","journal-title":"Phys Fluids"},{"key":"215_CR47_215","volume-title":"Lehrbuch der Theoretischen Physik, Bd. 6, Hydrodynamik","author":"L Landau","year":"1981","unstructured":"Landau L, Lifshitz EM (1981) Lehrbuch der Theoretischen Physik, Bd. 6,Hydrodynamik. Akademie, Berlin"},{"key":"215_CR48_215","unstructured":"Langner M, Peinke J, Rauh A () Langevin analysis with application toa\u00a0Rayleigh\u2013Benard convection experiment. Int J Nonlinear Dyn Syst Chaos (in press)"},{"key":"215_CR49_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-9018-6","volume-title":"Turbulence in fluids","author":"M Lesieur","year":"1997","unstructured":"Lesieur M (1997) Turbulence in fluids. Kluwer Academic Publishers, Dordrecht"},{"key":"215_CR50_215","volume-title":"New trends in turbulence, LesHouches Summer School","author":"M Lesieur","year":"2000","unstructured":"Lesieur M, Yaglom A, David F (2000) New trends in turbulence, LesHouchesSummer School. Springer, Berlin"},{"key":"215_CR51_215","doi-asserted-by":"crossref","unstructured":"L\u00fcck S, Renner C, Peinke J, Friedrich R (2006) The Markov\u2013Einsteincoherence length\u00a0\u2013 a\u00a0new meaning for the Taylor length in turbulence. Phys Lett A 359:335","DOI":"10.1016\/j.physleta.2006.06.053"},{"key":"215_CR52_215","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1063\/1.1762249","volume":"10","author":"TS Lundgren","year":"1969","unstructured":"Lundgren TS (1969) Distribution functions in the statistical theory ofturbulence. Phys Fluids 10:969","journal-title":"Phys Fluids"},{"key":"215_CR53_215","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1063\/1.863957","volume":"25","author":"TS Lundgren","year":"1982","unstructured":"Lundgren TS (1982) Strained spiral vortex model for turbulent finestructure. Phys Fluids 25:2193","journal-title":"Phys Fluids"},{"key":"215_CR54_215","doi-asserted-by":"crossref","first-page":"1472","DOI":"10.1063\/1.858585","volume":"A5","author":"TS Lundgren","year":"1993","unstructured":"Lundgren TS (1993) A\u00a0small-scale turbulence model. Phys Fluids A5:1472","journal-title":"Phys Fluids"},{"key":"215_CR55_215","doi-asserted-by":"crossref","DOI":"10.1142\/p349","volume-title":"Instabilities, chaos and turbulence","author":"P Manneville","year":"2004","unstructured":"Manneville P (2004) Instabilities, chaos and turbulence. Imperial College Press, London"},{"key":"215_CR56_215","volume-title":"two\u2010dimensional fluid dynamics. Lecture Notes in Physics","author":"C Marchioro","year":"1984","unstructured":"Marchioro C, Pulvirenti M (1984) Vortex methods in two\u2010dimensional fluiddynamics. Lecture Notes in Physics. Springer, Berlin"},{"key":"215_CR57_215","doi-asserted-by":"crossref","first-page":"2590","DOI":"10.1063\/1.1386937","volume":"13","author":"P Marcq","year":"2001","unstructured":"Marcq P, Naert AA (2001) Langevin equation for turbulent velocityincrements. Phys Fluids 13:2590","journal-title":"Phys Fluids"},{"key":"215_CR58_215","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1103\/PhysRevA.8.423","volume":"A8","author":"PC Martin","year":"1973","unstructured":"Martin PC, Siggia ED, Rose HA (1973) Statistical dynamics of classicalsystems. Phys Rev A8:423","journal-title":"Phys Rev"},{"key":"215_CR59_215","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198561606.001.0001","volume-title":"The physics of fluid turbulence","author":"WD McComb","year":"1990","unstructured":"McComb WD (1990) The physics of fluid turbulence. Clarendon Press, Oxford"},{"key":"215_CR60_215","first-page":"231","volume":"259","author":"HK Moffat","year":"1994","unstructured":"Moffat HK, Kida S, Ohkitani K (1994) Stretched vortices\u2014the sinews ofturbulence. J\u00a0Fluid Mech 259:231","journal-title":"J Fluid Mech"},{"key":"215_CR61_215","volume-title":"Statistical Fluid Mechanics: Mechanics of Turbulence","author":"AS Monin","year":"1971","unstructured":"Monin AS, Yaglom AM (1971) Statistical Fluid Mechanics: Mechanics ofTurbulence, vol\u00a01. MIT Press, Cambridge, MA"},{"key":"215_CR62_215","volume-title":"Statistical Fluid Mechanics: Mechanics of Turbulence","author":"AS Monin","year":"1975","unstructured":"Monin AS, Yaglom AM (1975) Statistical Fluid Mechanics: Mechanics ofTurbulence, vol\u00a02. MIT Press, Cambridge, MA"},{"key":"215_CR63_215","doi-asserted-by":"crossref","first-page":"214501","DOI":"10.1103\/PhysRevLett.87.214501","volume":"87","author":"N Mordant","year":"2001","unstructured":"Mordant N, Metz P, Michel O, Pinton J-F (2001) Measurement of Lagrangianvelocity in fully developed turbulence. Phys Rev Lett 87:214501","journal-title":"Phys Rev Lett"},{"key":"215_CR64_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9290-3","volume-title":"The N\u2011Vortex problem","author":"PK Newton","year":"2001","unstructured":"Newton PK (2001) The N\u2011Vortex problem. Springer, NewYork"},{"key":"215_CR65_215","volume-title":"Symmetrie, Invarianz und Selbst\u00e4hnlichkeit in der Turbulenz","author":"M Oberlack","year":"2000","unstructured":"Oberlack M (2000) Symmetrie, Invarianz und Selbst\u00e4hnlichkeit in derTurbulenz. Shaker, Aachen"},{"key":"215_CR66_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-2564-9","volume-title":"Theories of turbulence","author":"M Oberlack","year":"2002","unstructured":"Oberlack M, Busse FH (2002) Theories of turbulence. Springer,Wien"},{"key":"215_CR67_215","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0065-2687(08)60098-9","volume":"6","author":"AM Obukhov","year":"1959","unstructured":"Obukhov AM (1959) Description of turbulence in terms of Lagrangianvariables. Adv Geophys 6:113","journal-title":"Adv Geophys"},{"key":"215_CR68_215","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02780991","volume":"6","author":"L Onsager","year":"1949","unstructured":"Onsager L (1949) Statistical hydrodynamics. Suppl Nuovo Cimento6:279","journal-title":"Suppl Nuovo Cimento"},{"key":"215_CR69_215","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1017\/S0022112000001658","volume":"402","author":"S Ott","year":"2000","unstructured":"Ott S, Mann J (2000) An experimentalinvestigation of the relative diffusion of particle pairs in three\u2010dimensional turbulent flow. J\u00a0Fluid Mech 402:207","journal-title":"J Fluid Mech"},{"key":"215_CR70_215","volume-title":"The Kinematics of Mixing: Stretching, Chaos, and Transport","author":"JM Ottino","year":"1989","unstructured":"Ottino JM (1989) The Kinematics of Mixing: Stretching, Chaos, andTransport. Cambridge University Press, Cambridge"},{"key":"215_CR71_215","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03559-7","volume-title":"Turbulent flows, models and physics","author":"J Piquet","year":"1999","unstructured":"Piquet J (1999) Turbulent flows, models and physics. Springer,Berlin"},{"key":"215_CR72_215","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0360-1285(85)90002-4","volume":"11","author":"SB Pope","year":"1985","unstructured":"Pope SB (1985) Lagrangian PDF methods for turbulent flows. Annu Rev Fluid Mech26:23; Pope SB (1994) Pdf methods for turbulent reactive flows. Prog Energy Combust Sci 11:119","journal-title":"Prog Energy Combust Sci"},{"key":"215_CR73_215","volume-title":"Turbulent flows","author":"SB Pope","year":"2000","unstructured":"Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge"},{"key":"215_CR74_215","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1017\/S0022112001003597","volume":"433","author":"C Renner","year":"2001","unstructured":"Renner C, Peinke J, Friedrich R (2001) Experimental indications for Markovproperties of small scale turbulence. J\u00a0Fluid Mech 433:383","journal-title":"J Fluid Mech"},{"key":"215_CR75_215","doi-asserted-by":"crossref","first-page":"124502","DOI":"10.1103\/PhysRevLett.89.124502","volume":"89","author":"C Renner","year":"2002","unstructured":"Renner C, Peinke J, Friedrich R, Chanal O, Chabaud B (2002) Universality ofsmall scale turbulence. Phys Rev Lett 89:124502","journal-title":"Phys Rev Lett"},{"key":"215_CR76_215","first-page":"935","volume":"174","author":"O Reynolds","year":"1883","unstructured":"Reynolds O (1883) Philos Trans R Soc Lond 174:935","journal-title":"Philos Trans R Soc Lond"},{"key":"215_CR77_215","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1098\/rspa.1926.0043","volume":"110","author":"LF Richardson","year":"1926","unstructured":"Richardson LF (1926) Atmospheric diffusion shown ona\u00a0distance\u2010neighbour graph. Proc R Soc Lond A 110:709","journal-title":"Proc R Soc Lond A"},{"key":"215_CR78_215","doi-asserted-by":"crossref","first-page":"015302R","DOI":"10.1103\/PhysRevE.70.015302","volume":"70","author":"M Siefert","year":"2004","unstructured":"Siefert M, Peinke J (2004) Different cascade speeds for longitudinal andtransverse velocity increments of small-scale turbulence. Phys Rev E 70:015302R","journal-title":"Phys Rev E"},{"key":"215_CR79_215","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/14685240600677673a","volume":"7","author":"M Siefert","year":"2006","unstructured":"Siefert M, Peinke J (2006) Joint multi-scale statistics of longitudinal andtransversal increments in small-scale wake turbulence. J\u00a0Turbul 7:1","journal-title":"J Turbul"},{"key":"215_CR80_215","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1146\/annurev.fluid.29.1.435","volume":"29","author":"KR Sreenivasan","year":"1997","unstructured":"Sreenivasan KR, Antonia RA (1997) The phenomenology of small-scaleturbulence. Annu Rev Fluid Mech 29:435\u2013472","journal-title":"Annu Rev Fluid Mech"},{"key":"215_CR81_215","doi-asserted-by":"crossref","unstructured":"Sturman R, Ottino JM, Wiggins S (2006) The mathematical foundations ofmixing. In: Cambridge Monographs of Applied and Computational Mathematics, No 22","DOI":"10.1017\/CBO9780511618116"},{"issue":"2","key":"215_CR82_215","first-page":"196","volume":"20","author":"GI Taylor","year":"1921","unstructured":"Taylor GI (1921) Diffusion by continuous movement. Proc Lond Math Soc Ser20(2):196","journal-title":"Proc Lond Math Soc Ser"},{"key":"215_CR83_215","volume-title":"Infinite dimensional dynamical systems in mechanics and physics","author":"R Temam","year":"2007","unstructured":"Temam R (2007) Infinite dimensional dynamical systems in mechanics andphysics. Springer, Heidelberg"},{"key":"215_CR84_215","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1098\/rspa.1951.0179","volume":"208","author":"AA Townsend","year":"1951","unstructured":"Townsend AA (1951) On the fine structure of turbulence. Proc R Soc Lond A208:534","journal-title":"Proc R Soc Lond A"},{"key":"215_CR85_215","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1088\/1367-2630\/6\/1\/049","volume":"6","author":"M Tutkun","year":"2004","unstructured":"Tutkun M, Mydlarski L (2004) Markovian properties of passive scalar incrementsin grid\u2010generated turbulence. New J Phys 6:49","journal-title":"New J Phys"},{"key":"215_CR86_215","first-page":"951","volume":"55","author":"FR Ulinich","year":"1969","unstructured":"Ulinich FR, Ya Lyubimov B (1969) Statistical theory of turbulence of anincompressible fluid at large Reynolds numbers. Zh Exper Teor Fiz 55:951","journal-title":"Zh Exper Teor Fiz"},{"key":"215_CR87_215","unstructured":"Wilczek M, Jenko F, Friedrich R Lagrangian particle statistics in turbulentflows from a\u00a0simple vortex model. Phys Rev E (to appear)"},{"key":"215_CR88_215","unstructured":"Calculation performed by Wilczek M (M\u00fcnster)"},{"key":"215_CR89_215","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0003-4916(61)90056-2","volume":"14","author":"HW Wyld","year":"1961","unstructured":"Wyld HW (1961) Formulation of the theory of turbulence in incompressiblefluids. Ann Phys 14:143","journal-title":"Ann Phys"},{"key":"215_CR90_215","unstructured":"http:\/\/www.claymath.org\/millenium\/"}],"container-title":["Encyclopedia of Complexity and Systems Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-30440-3_215","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T05:58:35Z","timestamp":1739167115000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-30440-3_215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9780387758886","9780387304403"],"references-count":90,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-30440-3_215","relation":{},"subject":[],"published":{"date-parts":[[2009]]}}}