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  • Eddies
  • Turbulence
  • Springer  (2)
  • American Meteorological Society
  • MDPI Publishing
  • Nature P. G.
  • 1990-1994  (2)
  • 1992  (2)
Collection
Publisher
  • Springer  (2)
  • American Meteorological Society
  • MDPI Publishing
  • Nature P. G.
  • Wiley-Blackwell  (4)
Years
  • 1990-1994  (2)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 67 (1992), S. 203-228 
    ISSN: 1572-9613
    Keywords: Turbulence ; biorthogonal decomposition ; self-similarity ; fractals ; multifractals ; wavelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The scaling invariance of the Navier-Stokes equations in the limit of infinite Reynolds number is used to derive laws for the inertial range of the turbulence spectrum. Whether the flow is homogeneous or not, the spectrum is chosen to be that given by a well-chosen biorthogonal decomposition. If the flow is hoogeneous, this spectrum coincides with the classical Fourier (energy) spectrum which exhibits Kolmogorov's k−5/3 power law if the scaling exponent is assumed to be 1/3. In the more general case where the homogeneity assumption is relaxed, the spectrum is discrete and decays exponentially fast under the assumption that the flow is invariant (in a deterministic or statistical sense) under only one subgroup of the scaling coefficientλ of one scaling group of the equations (corresponding to one value of the scaling exponent). If the flow is invariant under two subgroups of scaling coefficientsλ andλ′, the spectrum becomes maximal, equal toR +. Finally, when a full symmetry, namely an invariance under a whole group, is assumed and the spectrum becomes continuous, the decaying law for the spectral density is derived and found to be independent of the specific value ofh These ideas are then applied to locally self-similar flows with multiple dilation centers (localized in space and time) and multiple scaling exponents, extending the concept of multifractals to space and time.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 68 (1992), S. 379-400 
    ISSN: 1572-9613
    Keywords: Lattice gas ; lattice Boltzmann ; three-dimensional flows ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The recent development of the lattice gas method and its extension to the lattice Boltzmann method have provided new computational schemes for fluid dynamics. Both methods are fully paralleled and can easily model many different physical problems, including flows with complicated boundary conditions. In this paper, basic principles of a lattice Boltzmann computational method are described and applied to several three-dimensional benchmark problems. In most previous lattice gas and lattice Boltzmann methods, a face-centered-hyper-cubic lattice in four-dimensional space was used to obtain an isotropic stress tensor. To conserve computer memory, we develop a model which requires 14 moving directions instead of the usual 24 directions. Lattice Boltzmann models, describing two-phase fluid flows and magnetohydrodynamics, can be developed based on this simpler 14-directional lattice. Comparisons between three-dimensional spectral code results and results using our method are given for simple periodic geometries. An important property of the lattice Boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency, while all other methods, including the spectral method, are unable to model complicated geometries efficiently.
    Type of Medium: Electronic Resource
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