Theoretical Model for Nonlinear Long Waves over a Thin Viscoelastic Muddy Seabed

I-Chi Chan
Additional contact information
I-Chi Chan: Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan

Mathematics, 2022, vol. 10, issue 15, 1-16

Abstract: We theoretically analyzed the interaction between surface water waves and a thin muddy seabed. Wave motion in the inviscid water layer was assumed to be irrotational and the soft mud was modeled as a linear viscoelastic fluid. Under the Boussinesq approximation for nonlinear long waves, we present a set of depth-integrated equations that can be solved for the depth-averaged horizontal water particle velocity and the free-surface displacement. The long wave model needs to be solved numerically in general. For the cases of linear progressive waves and solitary waves, further analytical solutions were obtained. The model-predicted wave amplitude attenuation rate was shown to reasonably agree with the field data. Our analysis suggests that the elasticity of mud can potentially enhance the wave damping efficiency of a muddy seabed. The present formulations generalize several existing linear and nonlinear models for the wave–mud problem reported in literature.

Keywords: long waves; muddy seabed; viscoelastic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/15/2715/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/15/2715/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:15:p:2715-:d:877812

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().