Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields

Frank W. Elliott, David J. Horntrop, Andrew J. Majda

Research output: Contribution to journalArticle

Abstract

Monte Carlo methods for computing various statistical aspects of turbulent diffusion with long range correlated and even fractal random velocity fields are described here. A simple explicit exactly solvable model with complex regimes of scaling behavior including trapping, subdiffusion, and superdiffusion is utilized to compare and contrast the capabilities of conventional Monte Carlo procedures such as the Fourier method and the moving average method; explicit numerical examples are presented which demonstrate the poor convergence of these conventional methods in various regimes with long range velocity correlations. A new method for computing fractal random fields involving wavelets and random plane waves developed recently by two of the authors [J. Comput. Phys. 117, 146 (1995)] is applied to compute pair dispersion over many decades for systematic families of anisotropic fractal velocity fields with the Kolmogorov spectrum. The important associated preconstant for pair dispersion in the Richardson law in these anisotropic settings is compared with the one obtained over many decades recently by two of the authors [Phys. Fluids 8, 1052 (1996)1 for an isotropic fractal field with the Kolmogorov spectrum.

Original languageEnglish (US)
Pages (from-to)39-48
Number of pages10
JournalChaos
Volume7
Issue number1
StatePublished - 1997

Fingerprint

Fractals
Monte Carlo method
Random Field
Velocity Field
tracers
Fractal
fractals
Monte Carlo methods
velocity distribution
Range of data
Turbulent Diffusion
Statistical Computing
Superdiffusion
Subdiffusion
Exactly Solvable Models
turbulent diffusion
Fourier Method
Moving Average
Scaling Behavior
Trapping

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Elliott, F. W., Horntrop, D. J., & Majda, A. J. (1997). Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields. Chaos, 7(1), 39-48.

Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields. / Elliott, Frank W.; Horntrop, David J.; Majda, Andrew J.

In: Chaos, Vol. 7, No. 1, 1997, p. 39-48.

Research output: Contribution to journalArticle

Elliott, FW, Horntrop, DJ & Majda, AJ 1997, 'Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields', Chaos, vol. 7, no. 1, pp. 39-48.
Elliott, Frank W. ; Horntrop, David J. ; Majda, Andrew J. / Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields. In: Chaos. 1997 ; Vol. 7, No. 1. pp. 39-48.
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