Erosion of Fluid Mud Layers. I: Entrainment Model

An entrainment model for fluid mud and soft mud is derived by integrating the equation of turbulent kinetic energy across the mixed layer and introducing some modeling assumptions. The resulting entrainment model is similar to models for mixed-layer deepening in lakes and reservoirs, but in addition accounts for settling and the work needed to entrain bed material. The conditions considered are such that the water layer is flowing, whereas the mud layer is at rest. The former layer is the turbulent mixed layer that erodes the quiescent mud layer. Such conditions may result from wind action or turbulence produced at other locations in the flow. The yield strength of the mud as well as the viscous drag of the mud layer due to the flow in the water layer are taken into account. Most empirical model coefficients are obtained from the literature. A sensitivity analysis shows that settling, bed strength, and viscosity all may substantially reduce entrainment rates. An experimental validation of the entrainment model developed is presented in a companion paper.