High-order structure functions for planet surfaces: A turbulence metaphor

IEEE Geoscience and Remote Sensing Letters

Volumn 2, Issue 3, 2005, Pages 362-365

  Nikora, Vladimir ^a  

^a NATIONAL INSTITUTE OF WATER AND ATMOSPHERIC RESEARCH   (New Zealand)

Author keywords

High order statistics; Multifractals; Planet surface; Scaling; Turbulence

Indexed keywords

FRACTALS; MATHEMATICAL MODELS; REYNOLDS NUMBER; SURFACE TOPOGRAPHY; TURBULENCE;

HIGH-ORDER STATISTICS; MULTIFRACTALS; PLANET SURFACE; SCALING;

PLANETARY SURFACE ANALYSIS;

EID: 27744553236     PISSN: 1545598X     EISSN: None     Source Type: Journal    
DOI: 10.1109/LGRS.2005.851553     Document Type: Article

References (22)

1. T. F. Stepinski, M. M. Marinova, P. J. McGovern, and S. M. Clifford, "Fractal analysis of drainage basins on Mars," Geophys. Res. Lett., vol. 29, no. 8, pp. 1-4, 2002. DOI: 10.1029/2002/GL014666.
2. N. Schorghofer and D. H. Rothman, "Acausal relations between topographic slope and drainage area," Geophys. Res. Lett., vol. 29, no. 13, pp. 1-4, 2002. DOI: 10.1029/2002GL015144.
3. T. F. Stepinski and S. Coradetti, "Comparing morphologies of drainage basins on Mars and Earth using integral-geometry and neural maps," Geophys. Res. Lett., vol. 31, no. L15604, pp. 1-4, 2004.
4. T. F. Stepinski, M. L. Collier, P. J. McGovern, and S. M. Clifford, "Martian geomorphology from fractal analysis of drainage networks," J. Geophys. Res., vol. 109, no. E2, E02005, pp. 1-12, 2004.
5. P. S. Dodds and D. H. Rothman, "Scaling, universality, and geomorphology," Annu. Rev. Earth Planet. Sci., vol. 28, pp. 571-610, 2000.
6. M. A. Kreslavsky and J. W. Head, III, "Kilometer-scale roughness of Mars: Results from MOLA data analysis," J. Geophys. Res., vol. 105, no. E11, pp. 26695-26711, 2000.
7. O. Aharonson, M. Zuber, and D. H. Rothman, "Statistics of Mars' topography from Mars orbiter laser altimeter: Slopes, correlations, and physical models," J. Geophys. Res., vol. 106, no. E10, pp. 23 723-23 735, 2001.
8. R. Orosei, R. Bianchi, A. Coradini, S. Espinasse, C. Federico, A. Ferriccioni, and A. I. Gavrishin, "Self-affine behavior of Martian topography at kilometer scale from Mars orbiter laser altimeter data," J. Geophys. Res., vol. 108, no. E4, 8023, pp. 1-10, 2003. DOI: 10.1029/2002JE001 883.
9. V. Nikora and D. Goring, "Mars topography: Bulk statistics and spectral scaling," Chaos, Solitons, Fractals, vol. 19, pp. 427-439, 2004.
10. _, "Martian topography: Scaling, craters, and high-order statistics," Math. Geol., vol. 37, no. 4, 2004.
11. D. Veneziano and V. Iacobellis, "Self-similarity and multifractality of topographic surfaces at basin and subbasin scales," J. Geophys. Res., vol. 104, no. B6, pp. 12 797-12 812, 1999.
12. U. Frisch, Turbulence. The Legacy of A.N. Kolmogorov. Cambridge, U.K.: Cambridge Univ. Press, 1995, ch. 8, pp. 120-192.
13. J. C. Davis, Statistics and Data Analysis in Geology. New York: Wiley, 1986, ch. 6, pp. 298-407.
14. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics. Cambridge, U.K.: Cambridge Univ. Press, 1997, ch. 8, pp. 181-214.
15. C. Paola, "Incoherent structure: Turbulence as a metaphor for stream braiding," in Coherent Flow Structures in Open Channel. New York: Wiley, 1996, pp. 705-723.
16. G. Parker, P. K. Haff, and A. B. Murray, "A Kolmogoroff-type scaling for the fine structure of drainage basins," Eos Trans. AGU, vol. 82, no. 47, 2001. H41D-08.
17. A.-L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth. Cambridge, U.K.: Cambridge Univ. Press, 1995, ch. 24, pp. 262-266.
18. V. Nikora and D. Goring, "On the relationship between Kolmogorov's and generalized structure functions in the inertial subrange of developed turbulence," J. Phys. A: Gen. Math., vol. 32, pp. 4963-4969, 1999.
19. 1/2 law and multifractal topography: Theory and analysis," Nonlinear Processes Geophys., vol. 2, pp. 16-22, 1995.
20. V. Nikora and D. Goring, "Sand waves in unidirectional flows: Scaling and intermittency," Phys. Fluids, vol. 12, no. 3, pp. 703-706, 2000.
21. _, "Extended self-similarity (ESS) in geological and geophysical applications," Math. Geol., vol. 33, no. 3, pp. 251-271, 2001.
22. R. Benzi, G. Amati, C. M. Casciola, F. Toschi, and R. Piva, "Intermittency and scaling laws for wall bounded turbulence," Phys. Fluids, vol. 11, no. 6, pp. 1284-1286, 1999.