Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping
A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the...
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| Published in | Applied mathematics and mechanics Vol. 32; no. 11; pp. 1357 - 1366 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Shanghai University Press
01.11.2011
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0253-4827 1573-2754 |
| DOI | 10.1007/s10483-011-1506-x |
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| Abstract | A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode. |
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| AbstractList | A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode. O353.2; A fractional-order Maxwell model is used to describe the viscoelastic seabed mud.The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model.The model is then used to investigate the effect of the mud on the surface-wave damping.The damping rate of a linear monochromatic wave is obtained.The elastic resonance of the mud layer is observed,which leads to the peaks in the damping rate.The damping rate is a sum of the modal damping rates,which indicates the wave damping induced by the mud motion of particular modes.The analysis shows that near the resonance,the total damping rate is dominated by the damping rate of the corresponding mode. |
| Author | 夏乐章 朱克勤 |
| AuthorAffiliation | Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China |
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| CitedBy_id | crossref_primary_10_1007_s12601_023_00102_5 crossref_primary_10_1016_S1001_6058_16_60608_X crossref_primary_10_1007_s10236_016_1027_y crossref_primary_10_1140_epjp_i2017_11371_6 crossref_primary_10_1038_s41598_023_45485_6 |
| Cites_doi | 10.1016/j.csr.2008.09.008 10.1029/2003JC001885 10.1142/9789812817747 10.1016/j.wavemoti.2010.05.001 10.1017/S0022112007005356 |
| ClassificationCodes | O353.2 |
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| Copyright | Shanghai University and Springer-Verlag Berlin Heidelberg 2011 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | O353.2 seabed mud 76A05 76B15 fractional-order Maxwell model wave-mud interaction wave damping |
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| Notes | A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode. 31-1650/O1 seabed mud, wave-mud interaction, wave damping, fractional-order Maxwell model Yue-zhang XIA , Ke-qin ZHU （Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China） |
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| References | Hilfer (CR5) 2000 CR3 Sheremet, Stone (CR1) 2003; 108 Liu, Chan (CR7) 2007; 579 Jiang, Mehta (CR4) 1995; 11 Jain, Mehta (CR2) 2009; 29 Xia, Zhu (CR6) 2010; 47 F. Jiang (1506_CR4) 1995; 11 A. Sheremet (1506_CR1) 2003; 108 P. L. F. Liu (1506_CR7) 2007; 579 R. Hilfer (1506_CR5) 2000 Y. Z. Xia (1506_CR6) 2010; 47 M. Jain (1506_CR2) 2009; 29 1506_CR3 |
| References_xml | – volume: 29 start-page: 642 issue: 3 year: 2009 end-page: 651 ident: CR2 article-title: Role of basic rheological models in determination of wave attenuation over muddy seabeds publication-title: Continental Shelf Research doi: 10.1016/j.csr.2008.09.008 – volume: 108 start-page: 3357 issue: C11 year: 2003 ident: CR1 article-title: Observations of nearshore wave dissipation over muddy sea beds publication-title: Journal of Geophysical Research doi: 10.1029/2003JC001885 – year: 2000 ident: CR5 publication-title: Applications of Fractional Calculus in Physics doi: 10.1142/9789812817747 – volume: 11 start-page: 918 issue: 3 year: 1995 end-page: 926 ident: CR4 article-title: Mudbanks of the southwest coast of India IV: mud viscoelastic properties publication-title: Journal of Coastal Research – ident: CR3 – volume: 47 start-page: 601 issue: 8 year: 2010 end-page: 615 ident: CR6 article-title: A study of wave attenuation over a Maxwell model of a muddy bottom publication-title: Wave Motion doi: 10.1016/j.wavemoti.2010.05.001 – volume: 579 start-page: 467 year: 2007 end-page: 480 ident: CR7 article-title: On long-wave propagation over a fluid-mud seabed publication-title: Journal of Fluid Mechanics doi: 10.1017/S0022112007005356 – volume: 11 start-page: 918 issue: 3 year: 1995 ident: 1506_CR4 publication-title: Journal of Coastal Research – volume: 108 start-page: 3357 issue: C11 year: 2003 ident: 1506_CR1 publication-title: Journal of Geophysical Research doi: 10.1029/2003JC001885 – ident: 1506_CR3 – volume: 47 start-page: 601 issue: 8 year: 2010 ident: 1506_CR6 publication-title: Wave Motion doi: 10.1016/j.wavemoti.2010.05.001 – volume: 579 start-page: 467 year: 2007 ident: 1506_CR7 publication-title: Journal of Fluid Mechanics doi: 10.1017/S0022112007005356 – volume: 29 start-page: 642 issue: 3 year: 2009 ident: 1506_CR2 publication-title: Continental Shelf Research doi: 10.1016/j.csr.2008.09.008 – volume-title: Applications of Fractional Calculus in Physics year: 2000 ident: 1506_CR5 doi: 10.1142/9789812817747 |
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| Snippet | A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the... O353.2; A fractional-order Maxwell model is used to describe the viscoelastic seabed mud.The experimental data of the real mud well fit the results of the... |
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| SubjectTerms | Applications of Mathematics Classical Mechanics Fluid- and Aerodynamics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Partial Differential Equations |
| Title | Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping |
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