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Modelling Contaminant Spread on the Ocean Surface and within Soils using fBm’s: Two Civil Engineering Applications

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Fractals in Engineering

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Abstract

A particle tracking method is outlined for modelling non-Fickian diffusion using fractional Brownian motions. Two environmental engineering applications of the model are presented, that is, the modelling of turbulent diffusion of spilled contaminants on the ocean surface and the sub/super-diffusive behaviour of contaminants in soils.

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References

  1. Hunter, J.R., Craig, P.D., Philips, H.E. (1993): On the Use of Random Walk Models with Spatially Variable Diffusivity. J. Comp. Phys., Vol. 106, 366–376.

    MATH  Google Scholar 

  2. Addison, P.S. (1996): A Method for Modelling Dispersion Dynamics in Coastal Waters Using Fractional Brownian Motion. IAHR Journal of Hydraulic Research, Vol. 34, No. 4, 549–561.

    Article  Google Scholar 

  3. Addison, P.S., Bo, Q. (8–10 September 1996): Modelling Fractal Diffusion on the Ocean Surface. In’Flow Modeling and Turbulence Measurements VI’, Proceedings of the 6th International Symposium on Flow Modeling and Turbulence Measurements, Tallahassee, Florida, USA, Balkema, 1996, 703–709.

    Google Scholar 

  4. Hurst, H.E. (1956): Methods of Using Long-Term Storage in Reservoirs. Proc. Inst. Civil Eng., Vol. 5, Part 1, 519–577.

    Google Scholar 

  5. Mandelbrot, B.B., Van Ness, J.W. (1968): Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, Vol. 10, 422–437.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yin, Z.-M. (1996): New Methods for Simulation of Fractional Brownian Motion. Journal of Computational Physics, Vol. 127, 66–72.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ozmidov, R.V. (1990): Diffusion of Contaminants in the Ocean. Kluwer Academic Publishers.

    Google Scholar 

  8. Okubo A. (1971): Oceanic Diffusion Diagrams. Deep Sea Research, Vol. 18, 789–802.

    Google Scholar 

  9. Sanderson, B.G., Booth, D.A. (1991): The Fractal Dimension of Drifter Trajectories and Estimates of Horizontal Eddy-Diffusivity. Tellus, Vol. 43A, 334–349.

    Google Scholar 

  10. Osborne A.R., Kirwan, A.D., Provenzale, A., Bergamasco, L. (1989): Fractal drifter Trajectories in the Kuroshio extension. Tellus, Vol. 41A, 416–435.

    Article  Google Scholar 

  11. List, E.J., Gartrell, G., Winant, CD. (1990): Diffusion and Dispersion in Coastal Waters. ASCE, Journal of Hydraulic Engineering, Vol. 116, 1158–1179.

    Article  Google Scholar 

  12. Jendele, L., Chan, A.H.C, Hellawell, E.E. (1995): Comparison of Software Modelling the Transport of Pollutants through Saturated Soil. Numerical Models in Geomechanics-NUMOG-V, G.N. Pande and S. Pietruszczak (editors), A.A. Balkema Publishers, 343–348.

    Google Scholar 

  13. Bartoli, F., Philippy, R., Doirisse, M., Niquet, S., Dubuit M. (1991): Structure and Self-Similarity in Silty and Sandy Soils: The Fractal Approach. Journal of Soil Science, Vol. 42, 167–185.

    Article  Google Scholar 

  14. Young, I.M., Crawford, J.W. (1991): The Fractal Structure of Soil Aggregates: Its Measurement and Interpretation. Journal of Soil Science, Vol. 42, 187–192.

    Article  Google Scholar 

  15. Toledo, P.G., Novy, R.A., Davis, H.T., Scriven, L.E. (1989): On the Transport Properties of Porous Media at Low Water Content. Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, Riverside, California, Oct. 11–13, 97–114. Edited by M.Th. van Genuchten, F.J. Leij and L.J. Lund.

    Google Scholar 

  16. Havlin S., Ben-Avraham D. (1987): Diffusion in Disordered Media. Advances in Physics, Vol. 36, No. 6, 695–798.

    Article  Google Scholar 

  17. Crawford, J.W., Ritz, K., Young, I.M. (1993): Quantification of Fungal Morphology, Gaseous Transport and Microbial Dynamics in Soil: An Integrated Framework Utilising Fractal Geometry. Geoderma, Vol. 56, 157–172.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Civil and Transportation Engineering, Napier University, Merchiston Campus, 10 Colinton Road, Edinburgh, EH10 5DT, Scotland, UK

    P. S. Addison & B. Qu

  2. Department of Civil Engineering, Glasgow University, The Rankine Building, Oakfield Avenue, Glasgow, G12 8LT, Scotland, UK

    A. Nisbet & G. Pender

Authors
  1. P. S. Addison
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  2. B. Qu
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  3. A. Nisbet
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  4. G. Pender
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Editor information

Editors and Affiliations

  1. INRIA-Rocquencourt, Domaine de Voluceau, BP 105, 78153, Le Chesnay Cedex, France

    Jacques Lévy Véhel  & Evelyne Lutton  & 

  2. Ecole Polytechnique de Montréal, Succ. Centre-Ville, CP 6079, H3C 3A7, Montréal, Québec, Canada

    Claude Tricot

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© 1997 Springer-Verlag London Limited

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Addison, P.S., Qu, B., Nisbet, A., Pender, G. (1997). Modelling Contaminant Spread on the Ocean Surface and within Soils using fBm’s: Two Civil Engineering Applications. In: Lévy Véhel, J., Lutton, E., Tricot, C. (eds) Fractals in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0995-2_28

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  • DOI: https://doi.org/10.1007/978-1-4471-0995-2_28

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1253-2

  • Online ISBN: 978-1-4471-0995-2

  • eBook Packages: Springer Book Archive

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