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Statistical Fluid Mechanics and Statistical Mechanics of Fluid Turbulence

TATSUMI, Tomomasa

Journal of physics. Conference series, 2011-12, Vol.318 (4), p.042024-11 [Periódico revisado por pares]

Bristol: IOP Publishing

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  • Título:
    Statistical Fluid Mechanics and Statistical Mechanics of Fluid Turbulence
  • Autor: TATSUMI, Tomomasa
  • Assuntos: Derivatives ; Dynamical systems ; Fluid dynamics ; Fluid flow ; Fluid mechanics ; Hypotheses ; Isotropic turbulence ; Mathematical analysis ; Navier-Stokes equations ; Nonlinearity ; Statistical analysis ; Statistical mechanics ; Turbulence ; Turbulent flow ; Velocity ; Velocity distribution
  • É parte de: Journal of physics. Conference series, 2011-12, Vol.318 (4), p.042024-11
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
  • Descrição: Turbulence in a fluid has two mutually contradictory aspects, that is, the apparent ran-domeness as a whole and the intrinsic determinicity due to the fluid-dynamical equations. In the traditional approarch to this subject, the velocity field of turbulence has been represented by the mean products of the turbulent velocities at several points and a time, and the equations governing the dynamical system composed of the mean velocity products are solved to obtain the mean velocity products as the deterministic functions in time. The works along this approach constitute the main body of turbulence research as outlined by Monin and Yaglom (1975) under the title of 'Statistical Fluid Mechanics'. It should be noted, however, that this approach has the diffculty of unclosedness of the equations for the mean velocity products due to the nonlinearity of the Navier-Stokes equations and an appropriate closure hypothesis is still awaited. In the statistical approach to turbulence, on the other hand, the random velocity field of turbulence is represented by the joint-probability distributions of the multi-point turbulent velocities. This approach has been taken by Lundgren (1967) and Monin (1967) independently, and the system of equations for the probability distributions of the multi-point velocities has been formulated. This system of equations is also unclosed, but in this case the problem is much easier to deal with since the unclosedness is not due to the nonlinearity but to the higher-order derivatives in the viscous term of the Navier-Stokes equations. Tatsumi (2001) proposed the cross-independence closure hypothesis for this purpose and proved its validity for homogeneous isotropic turbulence. More recently, the theory has extended by Tatsumi (2011) to general inhomogeneous turbulence and the closure is shown to provide an exact closure. This theory is outlined and discussed in the later part of this paper.
  • Editor: Bristol: IOP Publishing
  • Idioma: Inglês
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