In H-mode plasmas, two-dimensional steep structures of the electrostatic potential and density are formed when a large poloidal flow exists, whose formation mechanism has been studied to obtain a quantitative understanding of the particle transport in H-mode transport barriers. The previous two-dimensional model is extended to investigate parallel flow dynamics when potential and density distributions do not satisfy the Boltzmann relation. The extended model includes the generation mechanism of a poloidal shock structure and geodesic acoustic mode, whose competitive formation can be studied.