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A numerical model is extended to investigate the nonlinear dynamics of surface wave propagation over mud in the presence of currents. A phase-resolving frequency-domain model for wave-current interaction is improved to account for wave modulations due to viscoelastic mud of arbitrary thickness. The model compares well with published laboratory data and performs slightly better than the model with viscous mud-induced wave damping mechanism. Monochromatic and random wave simulations are conducted to examine the combined effect of currents, mud-induced wave dissipation and modulation, and nonlinear wave-wave interactions on surface wave spectra. Results indicate that current effects on wave damping over viscoelastic mud is not as straightforward as that over viscous mud. For example, while opposing currents consistently increase damping of random waves over viscous mud, they can decrease damping over viscoelastic mud due to high variations in frequency-dependent damping stemming from mud’s elasticity. It is shown that a model that assumes the mud layer to be thin for simplification can overestimate wave damping over thick mud layers.

Nonlinear Wave Evolution in Interaction with Currents and Viscoleastic Muds