Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

• Published in: Applied mathematics and mechanics Vol. 32; no. 11; pp. 1357 - 1366
• Main Author: 夏乐章 朱克勤
• 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: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; O353.2; seabed mud; 76A05; 76B15; fractional-order Maxwell model; wave-mud interaction; wave damping
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-011-1506-x

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.