以連續時間馬可夫鏈建立之序率輸砂模式

楊馥寧

doi:10.6342/NTU.2011.01856

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以連續時間馬可夫鏈建立之序率輸砂模式

STOCHASTIC MODELING OF BEDLOAD TRANSPORT BY THE CONTINUOUS-TIME MARKOV CHAIN PROCESS

楊馥寧 , Masters　　Advisor：蔡宛珊　　

英文 DOI： 10.6342/NTU.2011.01856

序率模式；馬可夫鏈；輸砂模式；泥沙交換；推移質； stochastic model ； Markov process ； bedload transport ； sediment transport ； sediment interchange

Abstract │ Reference (34) │ Altmetrics

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Based on the stochastic approach, a comprehensive Markov chain model for the sediment interchange process is performed in this study. The continuous-time Markov process is appropriate for describing the continuous behavior of particle movement under steady flow conditions. A certain mathematical formulation in employing the continuous-time Markov process is constructed by the presentation of a two-state Markov model for sediment entrainment. Then we accordingly propose a three-state continuous-time Markov model that completely simulates sediment exchange and thus can quantify the bedload transport rate more accurately. The three-state Markov model describes the particle movement across three motion states, i.e. bed material, bedload, and suspended load. We have added a third state to account for the influence of suspended load, which is different from general bedload transport studies. With the employment of the continuous-time Markov model, the bedload transport capacity in the long run and the varying transport rates with time before the steady state can be derived. On the other hand, the three-state model exhibits that the flow is subject to the bedload or suspended load and further the actual sediment distribution in three motion states. The proposed model is validated against the natural river data. The comparison has shown a reasonably good agreement and thus the validity is confirmed to some extent.

Reference ( 34 ) 〈TOP〉

[1] Abad J. D., Garcia M. H., “Discussion of “Efficient algorithm for computing Einstein Integrals” by Junke Guo and Pierre Y. Julien.” J. Hydraul. Eng., ASCE 2006; 132(3): 332-334 (J. Hydraul. Eng., ASCE 2004; 130(12): 1198-1201.
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[2] Ancey C., Bohm T., Jodeau M., Frey P., “Statistical description of sediment transport experiments.” Physical Review, 2006; 74(1): 011302(1-14).
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[3] Ancey C., Davison A. C., Bohm T., Jodeau M., Frey P., “Entrainment and motion of coarse particles in a shallow water stream down a steep slope.” J. Fluid Mech., 2008; 595: 83-114.
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[4] Ancey C., “Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions.” J. Geophysical Research, 2010; 115, F00A11: 1-21.
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[5] Beheshti A. A., Ataie-Ashtiani B., “Analysis of threshold and incipient conditions for sediment movement.” Coastal Eng., 2008; 55: 423–430.
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