Damping of waves propagating over a muddy bottom in deep water: Experiment and theory

• Deep water waves dissipate energy when it propagate over mud bottom.
• Experiments were conducted by generate wave groups to study energy dissipation.
• Develop expression for nonlinear interaction between two waves in deep water.
• Dissipation depends on wave periods and the bottom pressure of the bond long wave.

Surprisingly, deep water waves in the ocean propagating over mud bottoms can attenuate if wave groups are formed. This is shown in wave tank experiments, where two superimposed short waves with slightly different frequencies were generated to create the wave groups. Associated with the wave groups are long bound second order waves, which can exert wave pressure on the mud bottom, dissipating energy. Attenuation coefficients were measured by using Prony's method for each wave component as a function of distance down the tank. We develop an analytic expression for the nonlinear interaction between the two waves in deep water propagating at arbitrary angles by using Stokes' theory to second order. Finally, we show that the attenuation can be explained by the rate of work at bottom done by the long bound wave using the visco-elastic model MacPherson (1980). The results show that the dissipation depends on the incident wave periods, the bottom pressure and the vertical velocity of the long bound wave at the bottom.