The combined effect of wave–current interaction and mud-induced damping on nonlinear wave evolution

The development of a phase-resolving nonlinear frequency-domain model with both wave–current interaction and viscous mud-induced energy dissipation is discussed. The model is compared to dissipation rates deduced from experimental data, with favorable results. The model is then run with cnoidal waves over a finite mud patch with both opposing and following currents. It is determined that wave height dissipation by mud is exacerbated by opposing currents and reduced by following currents, in agreement with previous work. It is shown that mud-induced damping affects the cnoidal wave shape; under significant damping, the resulting waveform resembles a sine wave, with some short-scale variability as phase-locking between the harmonics breaks down. In addition, the effect of uncompensated subharmonic interactions, a cause of high frequency damping over mud, is also evident with wave–current interaction. Finally, random wave spectra are used to initialize the model and allowed to evolve over a flat bottom with a mud patch, with and without co-flowing currents. As before, the dissipation of the random waves is enhanced by opposing currents and reduced by following currents. The degree of spectral broadening seen in wave–current interaction in non-dissipative environments is also seen here with mud-induced dissipation. High spectral frequencies strongly damped by bottom mud recover some energy (at the expense of low frequencies) in the lee of the finite mud patch. This recovery is evident even with substantial damping across the majority of the frequency range of the spectrum.

► A nonlinear frequency domain model with mud dissipation and wave–current interaction is described.
► The model compares well with data from experiments of wave–current effects in mud dissipation.
► Following currents is found to reduce mud-induced dissipation, while opposing currents enhance it.
► The strong frequency dependence of mud dissipation is evident in the nonlinear evolution of the spectral shape.
► At high damping, the high frequencies rebound slightly in energy as the waves leave the mud patch.