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Structural Diffusion in 2D and 3D Random Flows

  • Nadeem A. Malik
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 36)

Abstract

We investigate one- and two-particle (relative) diffusion of fluid particles in incompressible 2D and 3D steady and unsteady random flows with prescribed self-similar power spectra of the form E(k) = C α ε * 2/3 kα for k min k(=|k|) ≤ k max and zero otherwise, for 1 < α < 3. C α is a constant, and ε* = εL1(5−3α)/2 where ε is the rate of energy dissipation per unit mass, and L1 is a length scale — in our work we choose L1 = 2π/k min . The role played by the streamline topology is of special interest. The velocity fields are generated using Kinematic Simulation (KS), Fung, Hunt, Malik & Perkins 1992, JFM 236, 281, viz
$$ \text{u}\left( {\text{x},t} \right) = \sum\limits_{n = 1}^{N_k } {\left\{ {\text{a}_n \cos \left( {k_n \cdot \text{x + }\omega _\text{n} t + \phi _n^a } \right) + \text{b}_n \sin \left( {k_\text{n} \cdot \text{x + }\omega _\text{n} t + \phi _n^b } \right)} \right\}} $$
and
$$ \text{a}_\text{n} \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{k} _n = \text{b}_n \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{k} _n = 0 $$
. The unsteadiness is proportional to the eddy-turnover frequency,
$$ \omega \left( k \right) = \lambda \in _*^{1/3} k^{\left( {3 - \alpha } \right)/2} $$
, and λ is a non-dimensional unsteadiness factor. The method of selecting the modes is described in the previous reference.
$$ \left\langle {u_i^2 } \right\rangle = 1 $$
, i = 1, 2 and also for i = 3 in 3D.

Keywords

Fluid Particle Inertial Range Previous Reference Structural Diffusion Kinematic Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Nadeem A. Malik
    • 1
  1. 1.L.M.F.A.Ecole Centrale de LyonEcullyFrance

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