Although analogies have been drawn between some types of meandering rivers and medium- to high-sinuosity, aggradational, leveed submarine channels, a number of different or additional processes operate in submarine channels. Analysis of several individual submarine channels suggests that they undergo much slower bend growth than alluvial rivers and may reach a planform equilibrium, in contrast to meandering rivers, in which bends progressively migrate downstream. Sinuous leveed submarine channels should therefore aggrade to produce isolated ribbons of thalweg deposits (of predictable 3D geometry), in contrast to the stacked channel belts characteristic of most alluvial meandering rivers. A simple model of the flow structure and flow evolution of turbidity currents traversing submarine channels is proposed, based on theoretical, experimental, and field-derived concepts. It predicts that submarine channel flows are highly stratified, have significant supra-levee thicknesses, and form broad overbank bodies of low-concentration fluid moving along the entire channel length. The interaction between the broad body of overbank fluid and within-channel flow is controlled by the processes of towing and angular shear, whose possible effects on channel sedimentation and planform stability are explored.