(untitled) (Advances in Applied Mathematics and Mechanics, 2023)
The meandering river is an unstable system with the characteristic of nonlinearity, which results from the instability of the flow and boundary. Focusing on the hydrodynamic nonlinearity of the bend, we use the weakly nonlinear theory and perturbation method to construct the nonlinear evolution equations of the disturbance amplitude and disturbance phase of two-dimensional flow in meandering bend. The influence of the curvature, Re and the disturbance wave number on the evolution of disturbance amplitude and disturbance phase are analyzed. Then, the spatial and temporal evolution of the disturbance vorticity is expounded. The research results show: that the curvature makes the flow more stable; that in the evolution of the disturbance amplitude effected by curvature, Re and the disturbance wave number, exist nonlinear attenuation with damping disturbances, and nonlinear explosive growth with positive disturbances; that the asymmetry distribution of the disturbance velocities increases with the curvature; that the location of the disturbance vorticity’s core area changes periodically with disturbance phase, and the disturbance vorticity gradually attenuates/increases with the decrease of the disturbance phase in the evolution process of damping/positive disturbances. These results shed light on the construction of the interaction model of hydrodynamic nonlinearity and geometric nonlinearity of bed.