Field observations from the spring of 2008 on the Louisiana shelf were used to elucidate the mechanisms of wave energy dissipation over a muddy seafloor. After a period of high discharge from the Atchafalaya River, acoustic measurements showed the presence of 20 cm thick mobile fluid-mud layers during and after wave events. While total wave energy dissipation (D) was greatest during the high energy periods, these periods had relatively low normalized attenuation rates (κ = Dissipation/Energy Flux). During declining wave-energy conditions, as the fluid-mud layer settled, the attenuation process became more efficient with high κ and low D. The transition from high D and low κ to high κ and low D was caused by a transition from turbulent to laminar flow in the fluid-mud layer as measured by a Pulse-coherent Doppler profiler. Measurements of the oscillatory boundary layer velocity profile in the fluid-mud layer during laminar flow reveal a very thick wave boundary layer with curvature filling the entire fluid-mud layer, suggesting a kinematic viscosity 2–3 orders of magnitude greater than that of clear water. This high viscosity is also consistent with a high wave-attenuation rates measured by across-shelf energy flux differences. The transition to turbulence was forced by instabilities on the lutocline, with wavelengths consistent with the dispersion relation for this two-layer system. The measurements also provide new insight into the dynamics of wave-supported turbidity flows during the transition from a laminar to turbulent fluid-mud layer.