Non-linear mechanics of ocean wave interactions with sediment beds

Abstract

The dispersion and attenuation of ocean wave spectra propagating over sloped poro-elastic beds with non-linear Coulomb internal damping are calculated using Biot's poro-elastic theory. Elastic properties and Coulomb dampings of sediments are functions of horizontal and vertical coordinates as well as the energy levels of wave spectra. The response of a seabed to water waves is characterized by a Mach number which is the ratio of the propagation velocity of the water wave to the local shear wave velocity. When the shear Mach number is small, as in sandy beds, the bed response is quasistatic and wave damping due to Coulomb internal damping in the soil is relatively small. When the shear Mach number approaches one, such as in normally consolidated clay, the bed motion is amplified dynamically, and the water wave damping due to the Coulomb internal friction becomes large compared to the damping owing to a turbulent boundary layer. The damping of water waves is very sensitive to wave height or wave energy level in this bed condition. Large waves damp out rapidly while small waves damp slowly. The shear Mach number becomes much larger than one in a very soft mud, which behaves as something like a ‘fluid’ with a Coulomb friction owing to the dynamic softening effect of clay under a large shear deformation. The wave damping becomes nearly independent of wave height or wave energy level in this bed condition. Soil-wave tank experiments substantiate the theoretical findings.