International Scientific Journal


This paper makes an attempt to develop a Hausdorff fractal derivative model for describing the vertical distribution of suspended sediment in unsteady flow. The index of Hausdorff fractal derivative depends on the spatial location and the temporal moment in sediment transport. We also derive the approximate solution of the Hausdorff fractal derivative advection-dispersion equation model for the suspended sediment concentration distribution, to simulate the dynamics procedure of suspended concentration. Numerical simulation results verify that the Hausdorff fractal derivative model provides a good agreement with the experimental data, which implies that the Hausdorff fractal derivative model can serve as a candidate to describe the vertical distribution of suspended sediment concentration in unsteady flow.
PAPER REVISED: 2017-11-24
PAPER ACCEPTED: 2017-11-27
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THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S109 - S115]
  1. Chien. N., Wan, Z.H., Mechanics of Sediment Transport, Science Press, Beijing, China, 2003
  2. Zhang, R. J., et al., River Dynamics, Wuhan University Press, Wuhan, China, 2007
  3. Dhamotharan, S., et al., Unsteady one Dimensional Settling of Suspended Sediment, Water Resources Research, 17 (1981), 4, pp.1125-1132
  4. Courtney K. Harris., Patricia L. Wiberg., A Two-dimensional, Time-dependent Model of Suspended Sediment Transport and Bed Reworking for Continental Shelves, Computers & Geosciences, 27 (2001), pp. 675-690
  5. Rouse, H., Modern Conceptions of the Mechanics of Fluid Turbulence, Transactions of the American Society of Civil Engineers, 102 (1937), 1, pp. 463-505
  6. Van Rijn, L.C., Mathematical Modeling of Suspended Sediment in Non-Uniform Flows. Journal of Hydraulic Engineering, 112 (1986), 6, pp. 433-455
  7. Nguyen, T.D., A Convection-Diffusion Model for Suspended Sediment in the Surf Zone, Journal of Geophysical Research, 102 (1997), C10, pp. 169-186
  8. Yu, D.S, Tian, C., Vertical Distribution of Suspended Sediment at the Yangze River Estuary, International Conference on Estuaries and Coasts, Hangzhou, China, 2003
  9. Soltanpour, M., Jazayeri, SMH., Numerical Modeling of Suspended Cohesive Sediment Transport and Mud Profile Deformation, Journal of Geophysical Research, 56 (2009), pp. 663-667
  10. Szymon, Sawczyński., Leszek M. Kaczmarek., Sediment Transport in the Coastal Zone, Technical Sciences, 17 (2014), 2, pp. 165-180
  11. Nguyen, V.T., Unsteady One-Dimensional Numerical Model for Prediction of Settling of Suspended Sediment, pp.1-6
  12. Chen, D., et al, Fractional Dispersion Equation for sediment Suspension, Journal of Hydrology, 491 (2013), 1, pp. 13-22
  13. Sun, H.G., et al, Anomalous Diffusion: Fractional Derivative Equation Models and Applications in Environmental Flows, Science China, 45 (2015), 10, pp.1-15 (in Chinese)
  14. Nie, S.Q., et al, Vertical Distribution of Suspended Sediment under Steady Flow: Existing Theories and Fractional Derivative Model, Discrete Dynamics in Nature and Society, (2017), pp.1-11
  15. Sun, H.G., et al, Fractional Differential Models for Anomalous Diffusion, Physica A, 389 (2010), pp. 2719-2724
  16. Baleanu, D., New Application of Fractional Variation Principles, Report on Mathematical Physics, 61 (2008), 2, pp. 199-206
  17. Zhang, Y., et al, A Subordinated Advection Model for Uniform Bed Load Transport from Local to Regional Scales, Journal of Geophysical Research, 119 (2014), 12, pp. 2711-2729
  18. Baleanu, D., Fractional Calculus: Models and Numerical Methods, World Scientific, 3 (2012), pp.10-16
  19. Chen, W., Time-Space Fabric underlying Anomalous Diffusion, Chaos, Solitons & Fractals, 28 (2006), 4, pp. 923-929
  20. Chen, W., et al., Anomalous Diffusion Modeling by Fractal and Fractional Derivatives, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1754-1758
  21. Liu, X.T., et al, A Variable-Order Fractal Derivative Model for Anomalous Diffusion, Thermal Science, 21 (2017), pp. 51-59
  22. Sun, H.G., et al, Fractional and Fractal Derivative Models for Transient Anomalous Diffusion: Model Comparison, Chaos, Solutions and Fractals, (2017), pp. 1-8
  23. Sun, H.G., et al, A Fractal Richards' Equation to Capture the non-Boltzmann Scaling of Water Transport in Unsaturated Media, Advances in Water Resources, 52 (2013), 4, pp. 292-295
  24. Sun, H.G., Chen, W., Fractal Derivative Multi-Scale Model of Fluid Particle Transverse Accelerations in Fully Developed Turbulence, Science in China Series E: Technological Sciences, 52 (2009), 3, pp. 680-683
  25. Liang, Y.J., et al, A Fractal Derivative Model for the Characterization of Anomalous Diffusion in Magnetic Resonance Imaging, Communications in Nonlinear Science & Numerical Simulation, 39 (2016), pp. 529-537
  26. Cai, W., et al, Characterizing the Creep of Viscoelastic Materials by Fractal Derivative Models, International Journal of Non-Linear Mechanics, 87 (2016), pp.58-63
  27. Reyes-Marambio, J., et al, A Fractal Time Thermal Model for Predicting the Surface Temperature of Air-Cooled Cylindrical Li-Ion Cells Based on Experimental Measurements, Journal of Power Sources, 306 (2016), pp. 636-645
  28. Chen, W., et al., Investigation on Fractional and Fractal Derivative Relaxation-Oscillation Models, International Journal of Nonlinear Sciences & Numerical Simulation, 11 (2010), 1, pp. 3-9
  29. Mishra, S., et al., Subdiffusion, Anomalous Diffusion and Propagation of Particle Moving on Random and Periodic Lorentz Lattice Gas, Journal of Statistical Phisics, 162 (2015), 4, pp. 1-15
  30. Leith, J.R., Fractal Scaling of Fractional Diffusion Processes, Signal Processing, 83 (2003), pp. 2397-2409
  31. Meerschaert, M. M., et al., Fractal Dimension Results for Continuous Time Random Walk, Statistics & Probability Letters, 83 (2013), 4, pp. 1083-1093
  32. Liu, D., et al., Fractal Analysis with Applications to Seismological Pattern Recognition of Underground Nuclear Explosion, Signal Processing, 80 (2000), pp. 1849-1861
  33. Van Genuchten, M. Th, Alves W. J., Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation, Document Delivery Servioes Branch USDA, National Agricultural Library 6th Floor, NAL BIdg 10301 Saltlmore Bivd Beitsville, MD 20705-2351, 1982
  34. Wei, X.T, et al., The Determination of Dispersion Coefficient by Convective-Dispersive Equation, Journal of Irrigation and Drainage, 19 (2000), 2, pp.48-51 (in Chinese)

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