On the simulation of continuous in scale universal multifractals, Part II: Space-time processes and finite size corrections

Computers and Geosciences

Volumn 36, Issue 11, 2010, Pages 1404-1413

  Lovejoy, S ^a,b   Schertzer, D ^c,d  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^c Universite Paris Est   (France)

^d MÉTÉO FRANCE   (France)

Author keywords

Fractals; Multifractals; Numerical simulations; Scaling; Turbulence

Indexed keywords

CASCADE PROCESS; COMPUTER TIME; FINITE SIZE EFFECT; FINITE-SIZE CORRECTIONS; MATHEMATICA; MEMORY USAGE; MULTIFRACTALS; NUMERICAL SIMULATION; SCALING; SMALL SCALE; SPACE TIME PROCESS; SPATIAL DISCRETIZATIONS; STATISTICAL PROPERTIES; TIME SIMULATIONS; UNIVERSAL MULTI-FRACTALS;

COMPUTER SIMULATION; FRACTALS; TURBULENCE;

MATHEMATICAL MODELS;

COMPUTER SIMULATION; FRACTAL ANALYSIS; NUMERICAL MODEL; TURBULENCE;

EID: 78149468270     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cageo.2010.07.001     Document Type: Article

References (24)

1. Bolgiano R. Turbulent spectra in a stably stratified atmosphere. Journal of Geophysical Research 1959, 64:2226-2229.
2. Charney J.G. Geostrophic turbulence. Journal of Atmospheric Science 1971, 28:1087-1091.
3. Corrsin S. On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. Journal of Applied Physics 1951, 22:469-473.
4. Gagnon J., Lovejoy S., Schertzer D. Multifractal earth topography. Nonlinear Processes in Geophysics 2006, 13:541-570.
5. Holschneider M. Wavelets: An Analysis Tool 1995, Clarendon Press, Oxford, New York.
6. Kolmogorov A.N. Local structure of turbulence in an incompressible liquid for very large Reynolds numbers. Proceedings of the Academy of Science of the USSR, Geochemistry Section 1941, 30:299-303. (English translation: Proceedings of the Royal Society A434, 9-17, 1991).
7. Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Physics of Fluids 1967, 10:1417-1423.
8. Lovejoy S., Schertzer D. Scaling and multifractal fields in the solid earth and topography. Nonlinear Processes in Geophysics 2007, 14:1-38.
9. Lovejoy S., Schertzer D. Towards a new synthesis for atmospheric dynamics: space-time cascades. Atmospheric Research 2010, 96:1-52. 10.1016/j.atmosres.2010.1001.1004.
10. Lovejoy S., Schertzer D., Allaire V., Bourgeois T., King S., Pinel J., Stolle J. Atmospheric complexity or scale by scale simplicity?. Geophysical Research Letters 2009, 36:L01801. Doi:01810.01029/02008GL035863.
11. Mandelbrot B.B How long is the coastline of Britain? Statistical self-similarity and fractional dimension. Science 1967, 155:636-638.
12. Obukhov A. Structure of the temperature field in a turbulent flow. Izvestia Akademie Nauk, SSSR, Serie Geographia I Geofizica 1949, 13:55-69.
13. Obukhov A. Effect of archimedean forces on the structure of the temperature field in a turbulent flow. Doklady Akademie Nauk SSSR 1959, 125:1246-1249.
14. Perrin J. Les Atomes 1913, NRF-Gallimard, Paris.
15. Richardson L.F. Weather Prediction by Numerical Process 1922, 1965. Cambridge University Press republished by Dover, 223 pp.
16. Richardson L.F. Atmospheric diffusion shown on a distance-neighbour graph. Proceedings of the Royal Society 1926, A110:709-737.
17. Richardson L.F. The problem of contiguity: an appendix of statistics of deadly quarrels. General Systems Yearbook 1961, 6:139-187.
18. Rodriguez-Iturbe I., Rinaldo A. Fractal River Basins 1997, Cambridge University Press, Cambridge, 547 pp.
19. Schertzer D., Lovejoy S. Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes. Journal of Geophysical Research 1987, 92:9693-9714.
20. Schertzer D., Lovejoy S., Hubert P. An introduction to stochastic multifractal fields. Mathematical Problems in Environmental Science and Engineering, Series in Contemporary Applied Mathematics 2002, vol. 4:106-179. Higher Education Press, Beijing.
21. Schertzer D., Lovejoy S., Lavallée D. Generic multifractal phase transitions and self-organized criticality. Cellular Automata: Prospects in Astronomy and Astrophysics 1993, 216-227. World Scientific. J.M. Perdang, A. Lejeune (Eds.).
22. Steinhaus H. Length, shape and area. Colloquium Mathematicum III 1954, 1-13.
23. Stolle J., Lovejoy S., Schertzer D. The stochastic cascade structure of deterministic numerical models of the atmosphere. Nonlinear Processes in Geophysics 2009, 16:1-15.
24. Szépfalusy P., Tél T., Csordas A., Kovas Z. Phase transitions associated with dynamical properties of chaotic systems. Physical Review A 1987, 36:3525-3538.