Autonomous vehicles provide a cost-effective, robust approach to tracking, surveillance and reconnaissance in land, air and sea. A cooperating team of vehicles maximizes the collected information by providing persistent, coordinated coverage of continuous and/or discrete spatiotemporal process. Much work has been done to provide control algorithms to promote collaboration of autonomous vehicles. One obstacle limiting the operational efficacy of these algorithms is their performance in the presence of external flow fields, such as tides or winds. For some platforms, these flow fields can represent a significant part of the vehicles inertial velocity. This research delves specifically into the collaborative control of autonomous vehicles for time-varying flow fields that can be either spatially uniform or non-uniform. In all cases it is assumed that the local flow field at the current time is known for each cooperating vehicle. We use a Newtonian-particle model to represent each vehicle. Each particle travels at a constant speed and is directed via a steering control that acts perpendicular to the particles velocity relative to the flow. We utilize a Lyapunov-based approach to develop decentralized control algorithms that stabilize a circular formation in a time-varying flow field. We provide a control law to create a circular formation about an arbitrary center and then introduce a symmetry-breaking particle that allows the center to be specified. The latter algorithm enables the particles to track maneuvering targets. We also provide a time-splay control law that regulates the spacing of the particles in the circular formation. Simulations are given to illustrate the capability to cooperatively encircle maneuvering targets that turn and accelerate.