Wave Interaction with Fluid Mud in Rectangular Trench

Wave interaction with fluid mud in a rectangular trench is studied theoretically based on small‐amplitude wave theory. The motion of fluid mud is modeled using the Voigt model for a viscoelastic medium. It is found that the elastic and viscous properties of a Voigt body result in a wide range of frictional characteristics and dynamic responses in the trench, depending on the magnitude of the elasticity parameter $m(G/{\rho }_2{\sigma }^2{)}^{1/2}$ and the viscosity parameter $m(v_2/\sigma {)}^{1/2}$. The relative importance of viscous effects and elastic effects is given by the ratio ${\mu }_2\sigma /G$, which is a wave frequency normalized by the retardation time of the Voigt material. For an almost rigid bed, where either the values of the elasticity parameter are high or the values of the viscosity parameter are high, amplitudes of mud waves are small and motions of surface waves are similar to those for homogeneous fluids. For a soft bed, when the frequency of incident waves corresponds to the natural frequency of mud waves, surface waves with relatively small amplitudes can result in large amplitude oscillations in the trench thus leading to more serious bed erosion. The response curve for the interfacial waves is very sensitive to viscous effects. As the depth of fluid mud decreases, viscous dissipation in the mud bed increases so wave amplitudes and shear stresses at the water‐mud interface decrease. This study indicates that the response of fluid mud to wave action may have significant effects on sedimentation characteristics in dredged navigation channels.