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

Chaos

Volumn 7, Issue 1, 1997, Pages 39-48

  Elliott Jr , Frank W ^a   Horntrop, David J ^a   Majda, Andrew J ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744450834     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166239     Document Type: Article

References (22)

1. 'G. Dagan, "Theory of solute transport by ground water," Annu. Rev. Fluid Mech. 19, 183(1987).
2. M. Lesieur, Turbulence in Fluids (Kluwer, Boston, 1990).
3. G. Csanady, Turbulent Diffusion in the Environment (Reidel, Dordrecht, Holland, 1973).
4. J. Feder, Fractals (Plenum, New York, 1988).
5. R. Voss, "Random fractal forgeries," in Fundamental Algorithms for Computer Graphics, edited by R. Earnshaw (Springer-Verlag, Berlin, 1985).
6. F. Elliott and A. Majda, "A wavelet Monte Carlo method for turbulent diffusion with many spatial scales," J. Comput. Phys. 113, 82 (1994).
7. F. Elliott and A. Majda, "A new algorithm with plane waves and wavelets for random advection diffusion," J. Comput. Phys. 117, 146 (1995).
8. L. Richardson, "Atmospheric diffusion shown on a distance-neighbor graph," Proc. R. Soc. London Ser. A 110, 709 (1926).
9. V. Tartarski, "Radiophysical methods of investigating atmospheric turbulence," Izv. Vyssh. Ucheb. Zaved. 3 Radiofiz. 4, 551 (1960).
10. F. Elliott and A. Majda, "Pair dispersion over an inertial range spanning many decades," Phys. Fluids 8, 1052 (1996).
11. D. Horntrop and A. Majda, "Subtle statistical behavior in simple models for random advection diffusion," J. Math. Sei. Univ. Tokyo 1, 23 (1994).
12. G. Matheron and G. de Marsily, "Is transport in porous media always diffusive? a counterexample," Water Resour. Res. 16, 901 (1980).
13. M. Avellaneda and A. Majda, "Mathematical models with exact renormalization for turbulent transport," Comm. Math. Phys. 131, 381 (1990).
14. I4M. Avellaneda and A. Majda, "Mathematical models with exact renormalization for turbulent transport II: non-Gaussian statistics, fractal interfaces, and the sweeping effect," Comm. Math. Phys. 146, 139 (1992).
15. I5M. Avellaneda and A. Majda, "Simple examples with features of renormalization for turbulent transport," Philos. Trans. R. Soc. Ser. A 346, 205 (1994).
16. J. Bouchaud, A. Georges, J. Koplik, A. Provata, and S. Redner, Phys. Rev. Lett. 64, 2503 (1990).
17. R. Zumofen, J. Klafter, and A. Blumen, J. Stat. Phys. 65, 991 (1991).
18. I8J. Viecelli and F. Canfield, "Functional representation of power-law random fields and time series," J. Comput. Phys. 95, 29 (1991).
19. K. Sabelfeld, Monte Carlo Methods (Springer-Verlag, New York, 1991).
20. D. Horntrop, Ph.D. thesis, Program in Applied and Computational Mathematics, Princeton University, 1995.
21. F. Elliott, A. Majda, D. Horntrop, and R. McLaughlin, "Hierarchical Monte Carlo methods for fractal random fields," J. Stat. Phys. 81, 717 (1995).
22. F. Elliott, D. Horntrop, and A. Majda, "A Fourier-wavelet Monte Carlo method for fractal random fields," to appear in J. Comput. Phys.