Results of an experimental study of geodesic acoustic modes (GAM) in the TUMAN-3M tokamak are reported. With Doppler backscattering (DBS) the basic properties of the GAM such as frequency, conditions for the GAM existence and the GAM radial location have been identified. The two-frequency Doppler reflectometer system was employed to reveal an interplay between low frequency sheared poloidal rotation, ambient turbulence level and the GAM intensity. Bicoherence analysis of the DBS data evidences the presence of a nonlinear interaction between the GAM and plasma turbulence.