I-CHI CHAN2023-05-042023-05-042022-08-012227-7390https://scholars.lib.ntu.edu.tw/handle/123456789/630782We 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.long waves | muddy seabed | viscoelastic[SDGs]SDG13[SDGs]SDG14journal article10.3390/math101527152-s2.0-85136823209WOS:000839809500001https://api.elsevier.com/content/abstract/scopus_id/85136823209