A numerical study on nonlinear surface wave evolution over viscoelastic mud

Accurate prediction of wave energy dissipation over mud is essential for understanding nearshore circulation, sediment transport processes, and design of engineering projects along muddy coasts. It is desirable to be able to simulate wave propagation over a wide range of mud behaviors as wave evolution is highly dependent on mud rheological characteristics. In this study, we develop a numerical model to simulate surface wave evolution over viscoelastic muds. This new wave-mud interaction model is comprised of a frequency-domain phase-resolving model for wave propagation that explicitly solves nonlinear wave-wave interactions, and a model for mud-induced surface wave dissipation and modulation. Model results show satisfactory agreement with laboratory measurements of wave height and attenuation rates over mud, and shows improvement over the model with a viscous mud mechanism. The model is then used to investigate the combined effect of mud viscoelasticity and nonlinear wave-wave interactions on surface wave evolution. Cnoidal and random wave simulations are conducted. In general, qualitative measures such as shape of cnoidal waves or pattern of variation in H-rms of random waves are dictated by direct mud-induced damping which due to resonance effects, has a substantially different structure over viscoelastic mud compared to viscous mud. Nonlinear interactions affect spectral shape and distribution of energy loss across the spectrum. Subharmonic interactions cause indirect damping of high frequencies but ameliorate damping of harmonics around mud's resonance frequency. Therefore, neglecting mud elasticity can result in significant errors in estimation of bulk wave characteristics and spectral shape.