Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend (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 onthe hydrodynamic nonlinearity of the bend, we use the weakly nonlinear theory andperturbation method to construct the nonlinear evolution equations of the disturbanceamplitude and disturbance phase of two-dimensional flow in meandering bend. Theinfluence of the curvature, $Re$ and the disturbance wave number on the evolution ofdisturbance 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 disturbanceamplitude effected by curvature, $Re$ and the disturbance wave number, exist nonlinearattenuation with damping disturbances, and nonlinear explosive growth with positivedisturbances; that the asymmetry distribution of the disturbance velocities increaseswith the curvature; that the location of the disturbance vorticity’s core area changesperiodically with disturbance phase, and the disturbance vorticity gradually attenuates/increases with the decrease of the disturbance phase in the evolution process ofdamping/positive disturbances. These results shed light on the construction of theinteraction model of hydrodynamic nonlinearity and geometric nonlinearity of bed.