Decentralized algorithms that stabilize three-dimensional formations of unmanned vehicles in a time-varying flowfield have applications in environmental monitoring in the atmosphere and ocean. This thesis provides Lyapunov-based algorithms to control a system of self-propelled particles traveling in three dimensions at a constant speed relative to a spatiotemporal flowfield. A particle's inertial velocity is the sum of its velocity relative to the flowfield plus the velocity of the flowfield. Multiple particles can be steered to form parallel, helical, and circular formations. A special case of the three-dimensional model is also studied, in which the particles travel on the surface of a sphere. In this case, we provide Lyapunov-based algorithms that stabilize circular formations in a time-varying flowfield on a rotating sphere. Because we are interested in using unmanned-vehicle formations for environmental monitoring, we simulate our results using numerical simulations of time-varying flowfields that resemble tornadoes and hurricanes.