Abstract: In recent years, the study of meandering river has shifted from linear characteristics to instability and nonlinear characteristics. Many researchers see the meandering river as an unstable system, for which they thought that the meandering river is mainly affected by the instability of the field flow and corresponding boundary. Aiming at the instability and nonlinear characteristics of the dynamics of the flow in meandering river, we make up the nonlinear evolution equations of flow disturbance amplitude and disturbance angle of constant curvature bend under the condition of weakly curve meandering, which were established by using the weakly nonlinear theory and perturbation method. In this paper we study the characteristics of disturbance development by considering different curvatures firstly, then discuss the spatial and temporal distribution characteristics of disturbed flow field under the influence of a series of curvatures, and expounds the influence of curvatures on the flow stability of curved river bend, in the end, we analyze the motion characteristics of disturbed vortex in disturbed flow field. We find that the increase of meandering bend curvature ratio will improve the stability of flow in the meandering bend, which is corresponding the others researchers' results. The disturbance amplitude and the disturbance angle of the flow decay faster with the increase of meandering curvature ratio, in the term of the symmetry of the disturbance velocity, which will become weaker with the increase of meandering curvature ratio and the incline to the convex bank of the bend when the meandering curvature ratio is larger. The flow dynamic of the meandering bend near the neutral state has the characteristics of convective instability and nonlinear attenuation. The research results in this paper provide a new idea for constructing a nonlinear interaction model of the nonlinear flow dynamics and the geometric nonlinearity of the meandering bed in the future research.