### 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 language | English (US) |
---|---|

Pages (from-to) | 39-48 |

Number of pages | 10 |

Journal | Chaos |

Volume | 7 |

Issue number | 1 |

State | Published - 1997 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Contribution to journal › Article

*Chaos*, vol. 7, no. 1, pp. 39-48.

}

TY - JOUR

T1 - Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields

AU - Elliott, Frank W.

AU - Horntrop, David J.

AU - Majda, Andrew J.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21744450834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744450834&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 39

EP - 48

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 1

ER -