Mass Transport Velocity of Bi-viscous Mud Under Progressive Waves

The mass transport of a thin layer of non-Newtonian bed mud under surface waves is examined using a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow fluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numerically. It is found that the stronger non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i.e., opposite to the wave propagation) for a certain range of the yield stress.