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Volume 38 Issue 7
Jul.  2012
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Journal of Beijing University of Aeronautics and Astronautics  > 2012  >  (7): 891-894,952.
Ran Zheng. Nature of vortex bifurcation and cascade in isotropic turbulence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, (7): 891-894,952. (in Chinese)
Citation: Ran Zheng. Nature of vortex bifurcation and cascade in isotropic turbulence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, (7): 891-894,952. (in Chinese)
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Nature of vortex bifurcation and cascade in isotropic turbulence

  • Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072, China

  • Received Date: 25 Jun 2011
  • Publish Date: 30 Jul 2012
    Abstract
  • The central problem of fully developed turbulence is understanding the energy cascading process and multiscale interaction. Update, there is no deductive theory which leads to a full physical understanding or mathematical formulation. The definition, development,challenge and the corresponding status of turbulence cascade were briefly reviewed. The limitation of present methods were emphasized. Based on the Karman-Howarth equation in 3D incompressible fluid, a new isotropic turbulence scale evolution equation and its related theory progress, the existence of nonlinear dynamic system measured by turbulence Taylor microscale was proven. The present results indicate that the energy cascading process has remarkable similarities with the determinisitic construction rules of the logistic map. The cascade appears as an infinite sequence of period-doubling vortex bifurcations.

     

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    • References(24)
  • [1]
    Monin A S,Yaglom A M.Statistical fluid mechanics vol2:mechanics of turbulence[M].Massachusetts:MIT Press,1975
    [2]
    Frisch U.Turbulence:the legacy of A N Kolmogorv[M].Cambridge:Cambridge University Press,1995
    [3]
    Richardson L F.Weather predicition by numerical process[M].Cambridge:Cambridge University Press,1922
    [4]
    Kolmogorov A N.The local structure of turbulence in incompressible visocus fluid for very large Reynolds numbers[J].Doklady Akademiia Nauk SSSR,1941,30:9-13
    [5]
    Kolmogorov A N.A refinement of previous hypotheses concerning the local strucutrue of turbulence in viscous incompressible fluid at high Reynolds number[J].J Fluid Mech,1962(13):82-85
    [6]
    Batchelor G K,Townsend A A.The nature of turbulent motion at large wave numbers[J].Proc R Soc Lond A 1949,199(1057):238-255
    [7]
    Obukhov A M.Some specific features of atmospheric turbulence[J].J Fluid Mech,1962(13):77-81
    [8]
    Novikov A A.Intermittency and scale similarity in the strcture of a turbulent flow[J].Prikl Mat Mech,1971(35):266-277
    [9]
    Mandelbrot B B.Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence[J].Statistical Models and Turbulance,1972,12:333-351
    [10]
    Novikov A A,Stewart R W.Intermittency of turbulence and the spectrum of fluctuations of energy dissipation[J].Izv Akad Nauk SSSR Geofiz,1964,3,408-413
    [11]
    Mandelbrot B B.Intermittent turbulence in self-similar cascades:divergence of high moments and dimension of the carrier[J].J Fluid Mech,1974,62:331-358
    [12]
    Kraichnan R H.On Kolmogorov’s inertial-range theories[J].J Fluid Mech,1974,62:305-330
    [13]
    Frisch U,Sulem P L,Nelkin M A simple dynamical model of intermittent fully developed turbulence[J].J Fluid Mech,1978,87:719-736
    [14]
    Lorenz E N.Deterministic nonperiodic flow[J].J Atmos Sci,1972,20:130-148
    [15]
    钱俭.混沌、湍流和非平衡统计力学[J].中国科学基金,1989(2):30-33
    Qian Jian.Chaos,turbulence and nonequilibrium statitistical mechanics[J].Chinese Natrual Science Foundations,1989(2):30-33(in Chinese)
    [16]
    Burgers J M.A mathematical model illustrating the theory of turbulence[J].Adv Appl Mech,1948,1:171-199
    [17]
    Desnyansky V N,Novikov E A.The evolution of turbulence spectra to the similarity regime[J].Izv Akad Nauk SSSR Fiz Atmos,1974,10:127-136
    [18]
    Kerr R M,Siggia E D.Cascade model of fully developed turbulence[J].J Stat Phys,1978,19:543-552
    [19]
    Gloaguen C,Leorat J,Pouquet A,et al.A scalar model for MHD turbulence[J].Physca D,1985,51:154-182
    [20]
    Qian J.Cascade model of turbulence[J].Phys Fluids,1988,31:2865-2874
    [21]
    Ran Z.New Sedov-type solution of isotropic turbulence[J].Chin Phys Lett,2008,25(12):4318-4320
    [22]
    Ran Z.One exactly soluble model in isotropic turbulence[J].Advances and Applications in Fluid Mechanics,2009,5(1),41-67
    [23]
    Ran Z.Remarks on Sedov-type solution of isotropic turbulence[EB/OL].New York:Cornell University Library,2009[2011-06-25].
    [24]
    Ran Z.Multiscales and cascading in isotropic turbulence[J].Chinese Sci Bull,2011,56:2889-2892
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