Hyperpycnal flows are turbid river plumes that can plunge to form turbidity currents where they enter a water body of lesser density. Because these flows provide one of the most direct connections between terrestrial sediment sources and marine depositional sinks, their deposits might preserve an important record across a variety of climatic and tectonic settings. A leading hypothesis assumes that hyperpycnal-flow velocity scales directly with river discharge, such that individual turbidites record the rising and falling discharge of a flooding river. We tested this hypothesis using a one-dimensional flow model and found that turbid river flow must move through a backwater zone, depth-limited plume, and plunging zone before becoming a turbidity current. These zones can extend tens of kilometers offshore and significantly affect the transfer of momentum from river to turbidity current. Counter to the proposed hypothesis, our results suggest that expected bed forms and sediment grading patterns in hyperpycnal-flow deposits can record multiple flow accelerations and decelerations even during a simple single-peaked flood. This occurs because of spatial acceleration and deceleration within the three transitional zones and because their boundaries move in response to flow discharge and suspended sediment concentration. Results also suggest that the criterion used to identify plunging hyperpycnal flows (a flow density in excess of the ambient fluid) is a necessary, but not sufficient condition. The basin also must be deep enough, in some cases greater than tens of meters, in order for the plume to collapse and form a turbidity current.