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Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows
Jean-Pierre Minier1, Christophe Profeta2
1EDF R&D, Mécanique des Fluides, Energie et Environnement, 6 quai Watier, 78400 Chatou, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
Summary
This study reveals that kinetic probability density function (PDF) models for particle dynamics in turbulent flows are incomplete and ill-posed due to non-Markovian processes and external noise. Proper variable selection is crucial for well-posed PDF descriptions.
Area of Science:
- * Fluid dynamics
- * Statistical mechanics
- * Computational physics
Background:
- * Analyzes two classical probability density function (PDF) descriptions for dispersed particles in turbulent flows.
- * Contrasts a kinetic PDF formulation (particle position and velocity) with a dynamic PDF formulation (including fluid variables).
- * Discusses high-Reynolds-number flow formulations using Langevin or Fokker-Planck models.
Purpose of the Study:
- * To derive a new kinetic PDF equation.
- * To obtain new physical expressions for dispersion tensors.
- * To demonstrate the relationship between kinetic and dynamic PDF descriptions.
Main Methods:
- * New derivation of the kinetic PDF equation.
- * Integration over fluid variables from the extended PDF.
- * Analysis of non-Markovian characteristics and external colored noise.
Main Results:
- * Kinetic PDF description is shown to be a marginal of a dynamic PDF description under Gaussian colored noise.
- * Kinetic PDF models are identified as incomplete and mathematically ill-posed for particle dynamics.
- * Ill-posedness is linked to non-Markovian processes and external colored noise.
Conclusions:
- * Kinetic PDF equations for particle dynamics in turbulent flows are mathematically ill-posed.
- * Well-posed PDF descriptions depend on the appropriate selection of system variables.
- * Emphasizes the importance of slow and fast variables for accurate PDF modeling.
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