Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement
The bed-load transport rates predicted using Einstein's formula in the low and high transport regimes deviate from the experimental data. The deviation, which becomes significant when the transport rate is extremely low or high, may be solely attributed to the folded Gaussian distribution assum...
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sg-ntu-dr.10356-1536762021-12-13T07:08:19Z Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement Wu, Haoliang Cheng, Nian-Sheng Chiew, Yee-Meng School of Civil and Environmental Engineering Engineering::Civil engineering Bed-Load Transport Einstein's Model The bed-load transport rates predicted using Einstein's formula in the low and high transport regimes deviate from the experimental data. The deviation, which becomes significant when the transport rate is extremely low or high, may be solely attributed to the folded Gaussian distribution assumed by Einstein. The trends of an Einstein-type formula at the limits can be separately determined by considering the limiting behavior of the embedded probability distribution, which facilitates the derivation of a formula that best fits the bed-load data. By applying a Gamma distribution with the shape parameter equal to 3/2, a modified Einstein's formula is successfully applied to the low and high transport regimes. Nanyang Technological University Published version The first author would gratefully acknowledge the financial support from the NTU Research Scholarship. The authors would also gratefully acknowl-edge the financial support from the National Natural Science Foundation of China (Grant No. 51979242), 2021-12-13T07:08:19Z 2021-12-13T07:08:19Z 2021 Journal Article Wu, H., Cheng, N. & Chiew, Y. (2021). Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement. Water Resources Research, 57(10), e2020WR028900-. https://dx.doi.org/10.1029/2020WR028900 0043-1397 https://hdl.handle.net/10356/153676 10.1029/2020WR028900 2-s2.0-85118251292 10 57 e2020WR028900 en Water Resources Research © 2021 American Geophysical Union. All Rights Reserved. This paper was published in Water Resources Research and is made available with permission of American Geophysical Union. application/pdf |
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Engineering::Civil engineering Bed-Load Transport Einstein's Model Wu, Haoliang Cheng, Nian-Sheng Chiew, Yee-Meng Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
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The bed-load transport rates predicted using Einstein's formula in the low and high transport regimes deviate from the experimental data. The deviation, which becomes significant when the transport rate is extremely low or high, may be solely attributed to the folded Gaussian distribution assumed by Einstein. The trends of an Einstein-type formula at the limits can be separately determined by considering the limiting behavior of the embedded probability distribution, which facilitates the derivation of a formula that best fits the bed-load data. By applying a Gamma distribution with the shape parameter equal to 3/2, a modified Einstein's formula is successfully applied to the low and high transport regimes. |
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School of Civil and Environmental Engineering |
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School of Civil and Environmental Engineering Wu, Haoliang Cheng, Nian-Sheng Chiew, Yee-Meng |
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Article |
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Wu, Haoliang Cheng, Nian-Sheng Chiew, Yee-Meng |
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Wu, Haoliang |
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Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
title_short |
Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
title_full |
Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
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Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
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Limiting behavior of the probability distribution in Einstein's bed-load formula and its improvement |
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limiting behavior of the probability distribution in einstein's bed-load formula and its improvement |
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2021 |
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https://hdl.handle.net/10356/153676 |
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