In subaerial and submarine meander bends, fluid flow travels downstream in a helical spiral, the structure of which is determined by centrifugal, hydrostatic, baroclinic, and Coriolis forces that together balance frictional stresses generated by the flow. The sense of rotation of this helical flow, and in particular, whether the near bed flow is directed toward the inner bank, e.g., "river-normal," or outer bank, e.g., "river-reversed," is crucial to the morphodynamic evolution of the channel. However, in recent years, there has been a debate over the river-normal or river-reversed nature of submarine flows. Herein, we develop a novel three-dimensional closure of secondary flow dynamics, incorporating downstream convective material transport, to cast new light on this debate. Specifically, we show that the presence of net radial material transport, arising from flow superelevation and overspill, exerts a key control on the near bed orientation of secondary flow in submarine meanders. Our analysis implies that river-reversed flows are likely to be much more prevalent throughout submarine-canyon fan systems than prior studies have indicated.