Spectral Collocation Model for Solitary Wave Attenuation and Mass Transport over Viscous Mud
Publication: Journal of Engineering Mechanics
Volume 135, Issue 8
Abstract
In this paper, wave attenuation and mass transport of a water-mud system due to a solitary wave on the free surface is modeled by using the Chebyshev-Chebyshev collocation spectral method for spatial discretization and a fourth-order multistage scheme for time integration. The governing equations are formulated in Lagrangian coordinates and perturbation equations for shallow water waves are derived. An iteration-by-subdomain technique is introduced to tackle the interface in the two-layer system. The numerical model is tested against available analytical solutions and good agreement has been found. Numerical simulations of the water-mud system with different layer thicknesses suggest that the accuracy of the existing boundary layer theory for fluid-mud interaction is limited when the mud layer is thin because the assumption of irrotational core may not be valid. Although the paper is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves over a non-Newtonian mud bottom.
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Acknowledgments
This study has been supported in part by grants from the Office of Naval Research Coastal Geosciences Program (N00014-07-1-0955) and the Louisiana Sea Grant College Program to Louisiana State University.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 8 • August 2009
Pages: 881 - 891
Copyright
© 2009 ASCE.
History
Received: Dec 27, 2007
Accepted: Jan 21, 2009
Published online: Jul 15, 2009
Published in print: Aug 2009
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