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This paper investigates the functional and morphological self-organization phenomena that occur during the bedform process in river systems. The fluvial process has architecturally functional self-organization actions that serve to self-adjust the river regime. The bedform (or sand waves) process is part of the functional self-organization at the middle level of the geometrical scale. By increasing the resistance of the mobile bed and simultaneously decreasing the capacity carrying sediment, the bedform serves to self-adjust the river system. The morphological self-organization of the bedform process is the basis for the functional self-organization. The concept of the water-sand interaction region is suggested, and a nonlinear model is constructed to describe the complex interaction among water flow, bed load transport, and local bed deformation, i. e., the sand waves. A numerical simulation was developed based upon this model. The primary results show that the model is able to repeat many important phenomena in the bedform process, especially the critical phase transition.