Dynamics of drift wave turbulence interacting with geodesic acoustic modes (GAMs) is investigated, focusing on the turbulence trapping in a phase space (real-space and wavenumber-space). Based on the wave-kinetic theory, we consider the dynamics of the turbulence coupling with the GAMs for two limiting cases; one is the case of GAMs driven by the turbulence, and the another is the case of the GAMs driven by energetic particles (EGAMs). For the case of the turbulence driven GAMs, the turbulence intensity is modulated spatially and temporally due to the trapping effect. The turbulence trapping significantly affects the spatial profile of the turbulence: The turbulence exclusion occurs at the positive curvature region, and the turbulence accumulation is significant at the negative curvature region. Their relation is kept with the propagation. It is also shown that the trapped turbulence by the EGAMs can be carried nonlocally in space. The trapped turbulence can penetrate the transport barrier and can propagate regions where the turbulence is stable. The turbulence trapping plays important roles for the nonlocal propagation of the turbulence and for determining the spatial profile of the turbulence intensity.