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 journalArticlepeer-review

20 Scopus citations


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
Issue number1
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


Dive into the research topics of 'Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields'. Together they form a unique fingerprint.

Cite this