Interaction between drift wave turbulence and streamer flow in magnetized plasmas is investigated in the framework of wave-kinetic theory. By performing a wave-kinetic simulation of turbulence coupling with the streamer flow, the role of the phase-space dynamics of turbulence is clarified. Here, the phase-space consists of the real space and wavenumber space. As a consequence of the phase-space dynamics, the turbulence is trapped in the flow and propagates with the streamer. Because of the trapping, the asymmetry of the turbulence intensity with respect to the sign of the flow curvature appears. The trajectories of the turbulence wave-packet, which are the characteristic curves of the wave-kinetic solution, can be categorized by the trapping, passing, and scattering. Therefore, the obtained phase-space structure of the turbulence can be understood by their trajectories. The propagation direction and speed are found to be governed by the turbulence spectrum. The obtained characteristics can be explained by the theoretical analysis.

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